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# Differential Equation for Mechanical System

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An electrophysiological recording table is subject to floor vibrations. Often each leg of such a table is placed on a "damper" consisting of a dashpot and spring in parallel. Assume that a dashpot and a spring are placed under each leg of the recording table, which has total mass M, so that the combined damping resistance is R and the combined spring constant is K.

(see attached diagram)

D(t) is the floor displacement and Y(t) is the resulting table displacement.
Write a differential equation for this mechanical system. The input is the up and down displacement of the floor and the output is the table displacement in the same direction. (Ignore lateral motions)

If M = 25 kg, K = 0.1 N/mm, and R = 100 N/m/s indicate whether it is over, under, or critically damped, and plot impulse response.

© BrainMass Inc. brainmass.com September 22, 2018, 6:05 am ad1c9bdddf - https://brainmass.com/physics/resistance/differential-equation-mechanical-system-71210

#### Solution Preview

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The equation of motion for the system: (for mass F=m*a; here the second derivative of Y(t) is the acceleration of table and the second derivative of D(t) is acc. of floor; for the spring, F=K*x, where K is the spring constant and x is the displacement; for the damper F=R*v, where v is for ...

#### Solution Summary

This solution contains a graph of impulse response and also step-by-step calculations with Matlab to determine if the system is underdamped, overdamped, or critically damped.

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