Q1. A first order system has a time constant of 4 sec and a steady state transfer function of 6. the Transfer function of first order system is ____________

A. G(s) = 6 / ( 4s+1) B. G(s) = 4 / ( 6 s + 1) C. G(s) = 1 / ( 6 s + 4) D. G(s) = s / ( 6 + 4s)

Check Answer

Correct Answer: A   |   Marks: 1

Explanation: A first-order system is written as G(s)=K/(τs+1). With steady-state gain K=6 and time constant τ=4 s, G(s)=6/(4s+1), which is option A.

Q2. A first order system has a time constant of 4sec and a steady state transfer function of 6. the equation of first order differential Equation is ____________

A. 4 dx/dt + x = 6y B. dx/dt + 4x = 6y C. dx/dt +6x = 4y D. 6dx/dt+ 4x = y

Check Answer

Correct Answer: A   |   Marks: 1

Explanation: For G(s)=K/(τs+1), the corresponding first-order equation is τ dx/dt+x=Ky. Substituting τ=4 s and K=6 gives 4 dx/dt+x=6y, option A.

Q3. A RLC circuit has a current i which varies with time t subjected to a step input of V is described by d^2i /dt^2 + 10 di/dt + 16 i = 16v. the given system behaves like a _____________

A. Over damped system. B. Under damped System C. Critically Damped System D. Un-Damped System

Check Answer

Correct Answer: A   |   Marks: 1

Explanation: The correct answer is option A. It follows from the principle or definition represented by that option: Over damped system.. The other options do not match the stated system relationship.

Q4. A RLC circuit has a current i which varies with time t subjected to a step input of V is described by d^2i /dt^2 + 10 di/dt + 16 i = 16v. the Damping Ratio of the system is ____________

A. 1.25 B. 0.8 C. 10 D. 4

Check Answer

Correct Answer: A   |   Marks: 1

Explanation: The correct answer is option A. It follows from the principle or definition represented by that option: 1.25. The other options do not match the stated system relationship.

Q5. A RLC circuit has a current i which varies with time t subjected to a step input of V is described by d^2i /dt^2 + 10 di/dt + 16 i = 16v. the un-damped frequency of the system is ____________

A. 4 Hz. B. 3 Hz C. 1 Hz D. 2 Hz

Check Answer

Correct Answer: A   |   Marks: 1

Explanation: The correct answer is option A. It follows from the principle or definition represented by that option: 4 Hz.. The other options do not match the stated system relationship.

Q6. A RLC circuit has a current i which varies with time t subjected to a step input of V is described by d^2i /dt^2 + 10 di/dt + 16 i = 16v. the Transfer function of the system is _______________

A. 16 / [ s^2 + 10 s + 16 ] B. 16 / [ 10s^2 + s + 16 ] C. 16 / [ s^2 + s + 16 ] D. 1 / [ s^2 + s + 1 ]

Check Answer

Correct Answer: A   |   Marks: 1

Explanation: The correct answer is option A. It follows from the principle or definition represented by that option: 16 / [ s^2 + 10 s + 16 ]. The other options do not match the stated system relationship.

Q7. An Accelerometer has a un damped frequency of 100Hz and a damping factor of 0.6. the maximum percentage of over shoot is _____________

A. 9.5 % B. 8.5 % C. 7 % D. 15 %

Check Answer

Correct Answer: A   |   Marks: 1

Explanation: For a second-order system, percentage overshoot is Mp=exp[-ζπ/√(1−ζ²)]×100. With ζ=0.6, the result is approximately 9.5%, so option A.

Q8. At time constant (ꚍ) the system output is equal to _________________

A. 0.632 Times of Steady state Response system. B. half of the Steady state response of the system. C. Total Steady state response of the system. D. Cannot Determine.

Check Answer

Correct Answer: A   |   Marks: 1

Explanation: For a first-order step response, y(t)=yss[1−e^(−t/τ)]. At t=τ, y/yss=1−e^−1≈0.632. Thus the output is 63.2% of the steady-state value, option A.

Q9. DC Motor is an example of ______________

A. Rotational translation system B. Electromechanical system C. Servo fluid system D. Hydro mechanical system

Check Answer

Correct Answer: B   |   Marks: 1

Explanation: A DC motor converts electrical input into mechanical rotational motion through electromagnetic action. Because electrical and mechanical domains are coupled, it is an electromechanical system, option B.

Q10. Hydraulic Press is an example of ______________

A. Rotational translation system B. Electromechanical system C. Servo fluid system D. Hydro mechanical system

Check Answer

Correct Answer: D   |   Marks: 1

Explanation: A hydraulic press uses pressurized fluid to transmit and amplify force. It is therefore classified as a hydro-mechanical system, option D.

Q11. If a systems are in parallel, the Overall transfer function is equal to the _____________________

A. Summation of transfer functions of individual systems B. Product of transfer functions of Individual systems C. Cannot say. D. infinity

Check Answer

Correct Answer: A   |   Marks: 1

Explanation: For parallel blocks, the same input is applied to each block and their outputs add algebraically. Hence the equivalent transfer function is the sum of the individual transfer functions, option A.

Q12. If a systems are in series Overall transfer function is equal to the _____________________

A. Sum of transfer functions of individual systems B. Product of transfer functions of Individual systems C. Cannot say. D. infinity

Check Answer

Correct Answer: B   |   Marks: 1

Explanation: For series or cascaded blocks, the output of one block becomes the input to the next. Therefore the overall transfer function is the product of the individual transfer functions, option B.

Q13. If the basic mathemetical equation of the second order system is 5 d^2 x/ dt^2 + 10 dx/dt + 16 x =16 F, the transfer function of the system is __________

A. 16 / [ 5s^2 + 10 s + 16 ] B. 1 / [ 5 s^2 + 10 s + 16 ] C. [ 5s^2 + 10 s + 16 ] / 16 F D. 16 / [ 10s^2 + 5 s + 16 ]

Check Answer

Correct Answer: A   |   Marks: 1

Explanation: Taking the Laplace transform of 5d²x/dt²+10dx/dt+16x=16F with zero initial conditions gives (5s²+10s+16)X(s)=16F(s). Thus X(s)/F(s)=16/(5s²+10s+16), option A.

Q14. If the basic mathemetical equation of the second order system is M d^2 x/ dt^2 + C dx/dt + Kx = F, the expressions of natural Frequency and Dammping Ratio are ___________

A. ωn = √ ( K/M) , ζ = √ ( C2/ 4MK) B. ωn = √ ( M/K) , ζ = √ ( C2/ 4K) C. ωn = √ ( 1/M) , ζ = √ ( C2/ MK) D. ωn = √ ( K/M) , ζ = √ ( C2)

Check Answer

Correct Answer: A   |   Marks: 1

Explanation: For M d²x/dt²+C dx/dt+Kx=F, comparison with the standard second-order form gives ωn=√(K/M) and ζ=C/(2√(MK))=√(C²/(4MK)). Hence option A.

Q15. if the basic second order system behaves a criticaly damped system subjected to the unit step input then the solution of system is ____________________

A. x (t) = A es1t+B es2t+ F / K B. (At+B) eωnt + F/K C. e-ζωnt ( P Cosωt + Q Sinωt) D. Cannot be find out

Check Answer

Correct Answer: B   |   Marks: 1

Explanation: A critically damped second-order system has repeated real poles. Its homogeneous response therefore contains a repeated-root term of the form (At+B)e^(−ωn t), together with the steady-state term F/K; this corresponds to option B.

Q16. if the basic second order system behaves a over damped system subjected to the unit step input then the solution of system is ____________________

A. x (t) = A es1t+B es2t+ F / K B. (At+B) eωnt + F/K C. e-ζωnt ( P Cosωt + Q Sinωt) D. Cannot be find out

Check Answer

Correct Answer: A   |   Marks: 1

Explanation: An overdamped system has two distinct real negative poles s1 and s2. Its response is therefore a sum of two exponential terms plus the steady-state value, A e^(s1t)+B e^(s2t)+F/K, option A.

Q17. if the basic second order system behaves a Under damped system subjected to the unit step input then the solution of system is ____________________

A. x (t) = A es1t+B es2t+ F / K B. (At+B) eωnt + F/K C. e-ζωnt ( P Cosωt + Q Sinωt) D. Cannot be find out

Check Answer

Correct Answer: C   |   Marks: 1

Explanation: An underdamped system has complex-conjugate poles. Its transient response is an exponentially decaying sinusoidal function, represented by e^(−ζωn t)(P cosωd t+Q sinωd t), corresponding to option C.

Q18. if the Damping ratio ( Ζ ) of the systems is equal to 1 then the system behaves like a _________________

A. Critically Damped System B. Under Damped System C. Over Damped System D. Un damped System

Check Answer

Correct Answer: A   |   Marks: 1

Explanation: A second-order system is critically damped when ζ=1. The poles are repeated real poles and the response returns to steady state without oscillation, so option A.

Q19. if the Damping ratio ( Ζ ) of the systems is equal to 1 then the system behaves like a _________________

A. Critically Damped System B. Under Damped System C. Over Damped System D. Un damped System

Check Answer

Correct Answer: A   |   Marks: 1

Explanation: A second-order system is critically damped when ζ=1. The poles are repeated real poles and the response returns to steady state without oscillation, so option A.

Q20. if the Damping ratio ( Ζ ) of the systems is equal to Zero then the system behaves like a _________________

A. Critically Damped System B. Under Damped System C. Over Damped System D. Un damped System

Check Answer

Correct Answer: D   |   Marks: 1

Explanation: When ζ=0, there is no damping. The poles are purely imaginary and the ideal system exhibits sustained oscillations, so it is an undamped system, option D.

Q21. if the Damping ratio ( Ζ) of the systems is greter than 1 then the system behaves like a _________________

A. Critically Damped System B. Under Damped System C. Over Damped System D. Un damped System

Check Answer

Correct Answer: C   |   Marks: 1

Explanation: When ζ>1, the two poles are real, distinct, and negative. The response does not oscillate and is classified as overdamped, option C.

Q22. if the Damping ratio ( Ζ) of the systems is less than 1 then the system behaves like a _________________

A. Critically Damped System B. Under Damped System C. Over Damped System D. Un damped System

Check Answer

Correct Answer: B   |   Marks: 1

Explanation: When 0<ζ<1, the poles form a complex-conjugate pair with negative real parts. The response oscillates with decreasing amplitude, so the system is underdamped, option B.

Q23. In Case of Fisrt order system representation the expressions for Time constant and System Gain is represented as _____________

A. Ꚍ = A1/A0 , G = B0/A0 B. Ꚍ = A0/A1 , G= B0/A1 C. Ꚍ = A1/A0 , G = A0/B0 D. Ꚍ = B1/A0 , G= B0/A0

Check Answer

Correct Answer: A   |   Marks: 1

Explanation: For A1 dx/dt+A0x=B0y, comparison with τ dx/dt+x=Ky gives τ=A1/A0 and system gain G=B0/A0. Therefore option A.

Q24. Inverse Laplace of [ a / s (s+a)] is _______________

A. 1 - E^(-AT) B. 1 - E^(-T) C. 1 - E D. 1 - E^(T)

Check Answer

Correct Answer: A   |   Marks: 1

Explanation: Using the partial-fraction result a/[s(s+a)]=1/s−1/(s+a), the inverse Laplace transform is 1−e^(−at). With time variable t, this corresponds to option A.

Q25. Laplace transformation of Unit Ramp function is ________________

A. 1/ S^2 B. 1/s C. 0 D. Infinity

Check Answer

Correct Answer: A   |   Marks: 1

Explanation: A unit ramp is r(t)=t for t≥0. Its Laplace transform is 1/s², so option A.

Q26. Laplace transformation of Unit step input function is ________________

A. 1 B. 1/s C. 0 D. Infinity

Check Answer

Correct Answer: B   |   Marks: 1

Explanation: A unit-step input is u(t)=1 for t≥0. Its Laplace transform is 1/s, so option B.

Q27. Laplase Transformation of Unit Impulse function is _________

A. 1 B. 0 C. Infinity D. 1/s

Check Answer

Correct Answer: A   |   Marks: 1

Explanation: The unit impulse δ(t) has the defining Laplace transform L{δ(t)}=1. Therefore option A.

Q28. Number of oscillation is define as the ratio of ________________

A. Settling time / Periodic Time B. Periodic Time/ Settling time C. Settling time * Periodic time D. Cannot Define

Check Answer

Correct Answer: A   |   Marks: 1

Explanation: The number of oscillations occurring during a settling interval is obtained by dividing settling time by the oscillation period. Hence number of oscillations=settling time/periodic time, option A.

Q29. Rack and pinion system is an example of ______________

A. Rotational translation system B. Electromechanical system C. Servo fluid system D. Hydro mechanical system

Check Answer

Correct Answer: A   |   Marks: 1

Explanation: A rack-and-pinion mechanism converts rotary motion of the pinion into linear motion of the rack. It is therefore a rotational-to-translational system, option A.

Q30. The expression for peak time is _________________

A. Π / (2Ω) B. Π / Ω C. 4/ (Ξ * ΩN) D. 3/ (Ξ * ΩN)

Check Answer

Correct Answer: B   |   Marks: 1

Explanation: For a standard underdamped second-order response, peak time is Tp=π/ωd, where ωd is the damped natural frequency. Thus option B.

Q31. The expression for rise time is _________________

A. Π / (2Ω) B. Π / Ω C. 4/ (Ξ * ΩN) D. 3/ (Ξ * ΩN)

Check Answer

Correct Answer: A   |   Marks: 1

Explanation: The rise time is the time required for the response to rise from its initial value toward the specified steady-state level. The source identifies π/(2ω) as the required expression, option A.

Q32. The Expression for Spring Element is _______________

A. F = Kx B. F = K / x C. F = x/K D. F = K

Check Answer

Correct Answer: A   |   Marks: 1

Explanation: A linear spring obeys Hooke's law: the restoring force is proportional to displacement. Thus F=Kx, where K is spring stiffness, so option A.

Q33. The state of damping of the system whose transfer function is represented as G(s)= [2s+1] / [s^2 + 2s +1] is _______________

A. Under damped System B. Over Damped System C. Critically damped System D. damped system

Check Answer

Correct Answer: C   |   Marks: 1

Explanation: The denominator is s²+2s+1=(s+1)². It has repeated real poles, corresponding to ζ=1 and a critically damped second-order system, option C.

Q34. The state of damping of the system whose transfer function is represented as G(s)= 10 / [s^2 + s +100].

A. Under damped System B. Over Damped System C. Critically damped System D. damped system

Check Answer

Correct Answer: A   |   Marks: 1

Explanation: Compare the denominator with s²+2ζωn s+ωn². Here ωn=10 rad/s and 2ζωn=1, giving ζ=0.05<1. Hence the system is underdamped, option A.

Q35. The Time at which ths response of the system reaches to 0.632 times of the steady state value is called ____________

A. Time Constant B. System Gain C. Dynamic response D. Cannot say

Check Answer

Correct Answer: A   |   Marks: 1

Explanation: For a first-order system, the response reaches 63.2% of its final value at t=τ. Therefore this characteristic time is called the time constant, option A.

Q36. The time constant of given system whose transfer function is G(s) = 3 / [2s+3]

A. 5 sec B. 3 sec C. 1 sec D. 0.67 sec

Check Answer

Correct Answer: D   |   Marks: 1

Explanation: Rewrite the transfer function as G(s)=1/[ (2/3)s+1]. Comparing with K/(τs+1), the time constant is τ=2/3≈0.67 s, option D.

Q37. The time constant of given system whose transfer function is G(s) = 5 / [3s+1]

A. 5 sec B. 3 sec C. 1 sec D. 0.6 sec

Check Answer

Correct Answer: B   |   Marks: 1

Explanation: The standard first-order form is K/(τs+1). Comparing 5/(3s+1) with this form gives τ=3 s and K=5, so option B.

Q38. The Time taken by the oscillations to died away is called _______________

A. Rise Time B. Peak Time C. Settling Time D. Peiodic Time

Check Answer

Correct Answer: C   |   Marks: 1

Explanation: Settling time is the time required for the transient response to decay and remain within a specified band around the final value. Thus option C.

Q39. The Time taken by the system to reach from zero to the first peak value is called _______________

A. Rise Time B. Peak Time C. Settling Time D. Peiodic Time

Check Answer

Correct Answer: B   |   Marks: 1

Explanation: Peak time is the time measured from the start of the response until the first maximum, or peak, value is reached. Hence option B.

Q40. The Time taken by the system to reach from zero to the steady state value is called _______________

A. Rise Time B. Peak Time C. Settling Time D. Peiodic Time

Check Answer

Correct Answer: A   |   Marks: 1

Explanation: Rise time describes how quickly a system response moves from its initial value toward its steady-state value. Therefore option A.

Q41. The total response of the system is equal to the ___________

A. Transient Responce + Steady state Response B. Transient Responce - Steady state Response C. Only Transient Response D. Product of Transient and Steady state Response

Check Answer

Correct Answer: A   |   Marks: 1

Explanation: The complete system response is the sum of its transient component and steady-state component: total response=transient response+steady-state response. Hence option A.

Q42. The Transfer Function of of RLC circuit in which output voltage is available across the resistor is _____________

A. RCs / [ LC s^2 + RCs + 1] B. RC / [ LC s^2 + RCs + 1] C. RCs / [ LC s + RCs^2 + 1] D. RCs / [ LC s^2 + 1]

Check Answer

Correct Answer: A   |   Marks: 1

Explanation: For a series RLC circuit with output across R, impedance division gives V_R/V_s=Rs/(Ls²+Rs+1). Multiplying numerator and denominator by the appropriate form gives RCs/(LCs²+RCs+1), option A.

Q43. The Transfer function of R L C Circuit in which output is available across the Capacitor is ________________

A. 1/ [LC s^2 + RC s + 1] B. 1/ [RC S^2 + LC s + 1] C. 1/ [LC s^2 + s + 1] D. 1/ [LC s^2 + 1]

Check Answer

Correct Answer: A   |   Marks: 1

Explanation: The correct answer is option A. It follows from the principle or definition represented by that option: 1/ [LC s^2 + RC s + 1]. The other options do not match the stated system relationship.

Q44. The Transfer function of RC Circuit in which out put is available across the capacitor is ____________

A. 1/ [RCs + 1] B. 1/ [s + RC] C. 1/ [RCs + RC] D. 1/RCs

Check Answer

Correct Answer: A   |   Marks: 1

Explanation: For a series RC circuit, the capacitor impedance is 1/(Cs). Voltage division gives V_C/V_in=1/(RCs+1), so option A.

Q45. Which of the following element of Mechanical Translaory element is euqalent to the Capacitor in Electrical system?

A. Spring B. Dashpot / Damper C. Mass Element D. Disc element.

Check Answer

Correct Answer: A   |   Marks: 1

Explanation: In force-voltage analogy, spring displacement corresponds to capacitor charge/voltage behavior because both store energy and their constitutive relations involve an integral-type relationship. Hence spring, option A.

Q46. Which of the following element of Mechanical Translaory element is euqalent to the Resistor in Electrical system?

A. Spring B. Dashpot / Damper C. Mass Element D. Disc element.

Check Answer

Correct Answer: B   |   Marks: 1

Explanation: In the force-voltage analogy, a mechanical dashpot/damper produces force proportional to velocity, analogous to the voltage drop across a resistor being proportional to current. Hence option B.

Q47. Which of the following is the expression for response of the First other system subjected to Unit step input?

A. X(T) = G [1 - E^ (-Ꚍ/T) ] B. X(T) = G[1 - E^ (-T) ] C. X(T) = 1 - E^ (-Ꚍ/T) D. X(T) = E ^ (-Ꚍ/T)

Check Answer

Correct Answer: A   |   Marks: 1

Explanation: For a first-order system G(s)=G/(τs+1), the unit-step response is x(t)=G[1−e^(−t/τ)]. The source represents this as option A.

Q48. Which of the following is the expression for Time constant and System gain ( Steady state value) of the first order system?

A. T= a1/a0 , G = b0/a0 B. T =a0/a1 , G = b0/a0 C. T =a1/a0 , G = b0/a1 D. T= a1/b0 , G = b0/a0

Check Answer

Correct Answer: A   |   Marks: 1

Explanation: For A1 dx/dt+A0x=B0u, comparison with τ dx/dt+x=Gu gives τ=A1/A0 and G=B0/A0. Hence option A.

Q49. Which of the Following is the laplace transfermation of First order derivative i.e Laplace [d f(t) / dt]

A. sF(s) - F(0) B. sF(0)-F(s) C. F(s) / s D. S^2 F(s) - s F(0) - d F(0)/ dt

Check Answer

Correct Answer: A   |   Marks: 1

Explanation: The Laplace transform of the first derivative is L{df/dt}=sF(s)−f(0). Therefore option A.

Q50. Which of the Following is the laplace transfermation of fisrt order integral function is

A. s*F(s) - F(0) B. s*F(0)-F(s) C. F(s) / s D. s^2* F(s) - s*F(0) - dF(0) / dt

Check Answer

Correct Answer: C   |   Marks: 1

Explanation: The correct answer is option C. It follows from the principle or definition represented by that option: F(s) / s. The other options do not match the stated system relationship.

Q51. Which of the Following is the laplace transfermation of Second order derivative i.e Laplace [d^2 f(t) / dt^2]

A. s*F(s) - F(0) B. s*F(0)-F(s) C. F(s) / s D. s^2* F(s) - s*F(0) - d F(0) / dt

Check Answer

Correct Answer: D   |   Marks: 1

Explanation: The Laplace transform of the second derivative is s²F(s)−s f(0)−f'(0). Thus option D.

Q52. Which of the following is the transfer function of Basic Mechanical Rotary system is _________________

A. 1/ [ J s^2 + Cs + K] B. 1/ [ Ms^2 + Cs + K] C. 1/ [ J s^2 + Ms + K] D. 1/ [ J s^2 + Ks + C]

Check Answer

Correct Answer: A   |   Marks: 1

Explanation: For a rotational mechanical system, the torque balance is Jθ''+Cθ'+Kθ=T. Taking Laplace transforms gives Θ(s)/T(s)=1/(Js²+Cs+K), option A.

Q53. Which of the Following is the Transfer function of Basic Spring, Mass and Damper system?

A. 1 / [Ms^2 + Cs + K] B. 1 / [Ms^2 + Cs] C. 1 / [s^2 + s + k] D. 1/[s^2 + s + 2]

Check Answer

Correct Answer: A   |   Marks: 1

Explanation: For translational motion, Newton's law gives Mx''+Cx'+Kx=F. With zero initial conditions, X(s)/F(s)=1/(Ms²+Cs+K), option A.

Q54. Which of the following the definition of Transfer Function?

A. Ratio of Output to the Input. B. Product of Input and Output Functions. C. Ratio of Laplace transfermation of Output to the Laplace transfermation of Input D. Cannot define

Check Answer

Correct Answer: C   |   Marks: 1

Explanation: A transfer function is defined, for zero initial conditions, as the ratio of the Laplace transform of the output to the Laplace transform of the input. Hence option C.

Q55. Which of the follwing are the basic Elements of Electrical system Modelling?

A. Spring, Mass, and Damper B. Torsion Spring, Rotating Damper and Disc C. Resistor, Capacitor and inductor D. Thermal Resistance and Thermal capacitance

Check Answer

Correct Answer: C   |   Marks: 1

Explanation: The fundamental lumped elements used to model electrical systems are the resistor, capacitor, and inductor. Therefore option C.

Q56. Which of the follwing are the basic Elements of Mechanical Translator systems?

A. Spring, Mass, and Damper B. Torsion Spring, Rotating Damper and Disc C. Resistor, Capacitor and inductor D. Thermal Resistance and Thermal capacitance

Check Answer

Correct Answer: A   |   Marks: 1

Explanation: A basic translational mechanical model uses mass to represent inertia, a spring to store elastic energy, and a damper to dissipate energy. Hence option A.

Q57. Which of the follwing are the basic Elements of Thermal system?

A. Spring, Mass, and Damper B. Torsion Spring, Rotating Damper and Disc C. Resistor, Capacitor and inductor D. Thermal Resistance and Thermal capacitance

Check Answer

Correct Answer: D   |   Marks: 1

Explanation: Thermal systems are commonly modeled using thermal resistance and thermal capacitance, representing heat-flow opposition and thermal energy storage respectively. Hence option D.

Q58. Which of the follwoing is the Mathemetical Equation of Mechanical Rotary System?

A. M*d^2 x/ dt^2+c* dx/dt + kx = Fin B. T in= J α + k θ + c ω C. Vs = RC dVc/dt + LC d^2 Vc/ dt^2 + Vc D. [L/R] d/dt [Vr]+ [1/RC] ∫Vr dt + Vr

Check Answer

Correct Answer: B   |   Marks: 1

Explanation: For rotational mechanical motion, the torque balance is T_in=Jα+Cω+Kθ. Here J is moment of inertia, C is rotational damping coefficient, and K is torsional stiffness, so option B.

Q59. Which of the follwoing is the Mathemetical Equation of RLC Circuit in which Output is avaliable across the Resistor?

A. M*d^2 x/ dt^2+c* dx/dt + kx = Fin B. T in= J α + k θ + c ω C. Vs = RC dVc/dt + LC d^2 Vc/ dt^2 + Vc D. [L/R] d/dt [Vr]+ [1/RC] ∫ Vr dt + Vr

Check Answer

Correct Answer: D   |   Marks: 1

Explanation: For the RLC circuit with output across the resistor, the governing equation in the source is [L/R]dV_R/dt+[1/(RC)]∫V_Rdt+V_R=V_s. Hence option D.

Q60. Which of the follwoing is the Mathemetical Equation of RLC Circuit in which Output is avaliable across the Capacitor?

A. M*d^2 x/ dt^2+c* dx/dt + kx = Fin B. T in= J α + k θ + c ω C. Vs = RC dVc/dt + LC d^2 Vc/ dt^2 + Vc D. [L/R] d/dt [Vr]+ [1/RC] ∫ Vr dt + Vr

Check Answer

Correct Answer: C   |   Marks: 1

Explanation: For output across the capacitor, the source gives V_s=RC dV_C/dt+LC d²V_C/dt²+V_C. This follows from the series RLC voltage balance, so option C.

Q61. Which of the follwoing is the Mathemetical Equation of Spring Mass and damper systems?

A. M*d^2 x/ dt^2+c* dx/dt + kx = Fin B. T in= Jα + kθ + cω C. Vs = RC dVc/dt + LC d^2 Vc/ dt^2 + Vc D. [L/R] d/dt [Vr]+ [1/RC] ∫Vr dt + Vr

Check Answer

Correct Answer: A   |   Marks: 1

Explanation: The governing equation for a translational spring-mass-damper system follows Newton's second law: Mx''+Cx'+Kx=F_in. Therefore option A.

Q62. Which of the governing equations are required to generate the mathemetical equations of Elecetrical system?

A. Krichoff's Laws. B. Faradays Law of electricity. C. Momentum equation. D. Newtion equation of Motion.

Check Answer

Correct Answer: A   |   Marks: 1

Explanation: The correct answer is option A. It follows from the principle or definition represented by that option: Krichoff's Laws.. The other options do not match the stated system relationship.