Question

A mass of 50 kg is supported by an elastic structure of total stiffness 20 KN/m. The

damping ratio of the system is 0.2. A simple harmonic disturbing force acts on the mass and

at any time t seconds, the force is 60 sin10t newtons. Find the amplitude of the vibration and

the phase angle caused by the damping​

Answer 1

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A body of mass 20 kg is suspended from a spring which deflects 15

mm under this load. Calculate the frequency of free vibrations and verify that a

viscous damping force amounting to approximately 1000 N at a speed of 1 m/s is

just-sufficient to make the motion aperiodic. If when damped to this extent, the

body is subjected to a disturbing force with a maximum value of 125 N making 8

cycles/s, find the amplitude of the ultimate motion.

Solution. Given: m = 20 kg; = 15 mm = 0.015 m ; c = 1000 N/m/s ; F = 125 N;

f = 8 cycles/s

Frequency of free vibrations

We know that frequency of free vibrations,