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Simple Harmonic Motion Problem Set

A) A mass of 25kg is supported by a vertical spring of stiffness 25kN/m and is acted on by a periodic force which has an amplitude 50N and frequency 5Hz. determine the steady state amplitude of the force vibration and the maximum force acting on the support point for the spring.

b) A horizontal platform rests on four vertical springs, each of stiffness 15kN/m and mass 0.25kg. what will the frequency of oscillation of the table be if it has a mass of 2.okg

Solution Preview

For the first question what you should do first is to make a force balance among the inertial forces, the spring force, the mass weight and the variable force. That give you the following equation :

M * d2y/dt2 + K*y = M*g + F*cos(w*t)

I am assuming the variable force is a cosin function of time.

If you solve ...

Solution Summary

The first question is solved by balancing the inertial forces, the spring force, the mass weight and the variable force. The answer for the second question is obtained using the balance for equation M d2y/dt2 + c * dy/dt + K * y = 0. 175 words.

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