7/26/2019 MEC 522 Tutorial2

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MEC 521: Vibration

Free Vibration

1.  When a 2 kg cylinder is suspended from a spring, the spring is stretched by a distance

of 40 mm. What will be the natural frequency (in Hz) and the period of vibration for a0.5 kg cylinder suspended from the same spring?

 

2.  A 25 N weight is suspended from a spring which has a stiffness k  = 0.42 Nmm-1. The

weight is given an upwards velocity of 5 ms-1 when it is 40 mm above its equilibrium

 position. Determine the equation for the motion of the weight, and its maximum

upward displacement. Assume positive displacement is downward. 

3.  A 200 kg machine is placed at the end of a 1.8 m long steel (  E  = 210 x 109 N/m2)

cantilever beam. The machine is observed to vibrate with natural frequency of 21 Hz.

What is the moment of inertia of the beam’s cross section about its neutral axis? 

4.  A 2.5 kg slender bar of length 40 cm is pinned at one end. A 3 kg particle is to be

attached to the bar. How far from the pin support should the particle be placed such

that the period of the bar’s oscillation is 1 s? 

5.  The addition of damping to an initially undamped spring-mass system increases the

 period of vibration by 15%. Find the value of the damping ratio.

6.  A mass of 2 kg is supported by a damped spring, where the damping constant is 2.8

 Nsm-1. The mass is displaced 20 mm from its equilibrium position and released from

rest, and the frequency is observed to be 2.5 Hz. Find (a) the displacement after 5complete cycles (b) the time taken for the displacement to be reduced to 5% of the

initial displacement.