61. A vehicle suspension system consists of a spring and a damper. The stiffness of the spring is 3.6 kN/m and the damping constant of the damper is 400 Ns/m. If the mass is 50 kg, then the damping factor (d) and damped natural frequency (fn), respectively, are

1. 1. 0.471 and 1.19 Hz

   
   
   

   2. 0.471 and 7.48 Hz

   
   
   

   3. 0.666 and 1.35 Hz

   
   
   

   4. 0.666 and 8.50 Hz

   
   
   

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   Damping factor
   

   =	C
   	2√sm

   
   

   =	400	= 0.741
   	2√50 × 3.6 × 103

   
   ω_d = (√1 - ξ²)ω_n
   ω_d = √1 - (471)²× 8.481
   ω_d = 7.48
   

   Nd =	ωd	=	7.48	= 1.19 Hz
   	2π		2 × 3.14

   Correct Option: A

   Damping factor
   

   =	C
   	2√sm

   
   

   =	400	= 0.741
   	2√50 × 3.6 × 103

   
   ω_d = (√1 - ξ²)ω_n
   ω_d = √1 - (471)²× 8.481
   ω_d = 7.48
   

   Nd =	ωd	=	7.48	= 1.19 Hz
   	2π		2 × 3.14

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62. An automotive engine weighing 240 kg is supported on four springs with linear characteristics. Each of the front two springs have a stiffness of 16 MN/m while the stiffness of each rear spring is 32 MN/m. The engine speed (in rpm), at which resonance is likely to occur, is

1. 1. 6040

   
   
   

   2. 3020

   
   
   

   3. 1424

   
   
   

   4. 955

   
   
   

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   Correct Option: A

   

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63. The equation of motion of a harmonic oscillator is given by
    
    and the initial conditions at t = 0 are x(0) = X,
    

    	dx	(0) = 0.
    	dt

    
    The amplitude of x(t) after n complete cycles is

1. 1. 

   
   
   

   2. 

   
   
   

   3. 

   
   
   

   4. X

   
   
   

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   Correct Option: A

   

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64. The value of logarithmic decrement is

1. 1. 1.35

   
   
   

   2. 1.32

   
   
   

   3. 0.42

   
   
   

   4. 0.66

   
   
   

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   Logarithmic decrement,
   

   Correct Option: C

   Logarithmic decrement,
   

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65. The value of critical damping of the system is

1. 1. 0.223 Ns/m

   
   
   

   2. 17.88 Ns/m

   
   
   

   3. 71.4 Ns/m

   
   
   

   4. 223.6 Ns/m

   
   
   

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   For critical damping,
   

   Correct Option: D

   For critical damping,
   

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