A simple pendulum has a length l of 1 m in free vibration

Reference no: EM13585357

A simple pendulum has a length (l) of 1 m. In free vibration the amplitude of its swings falls off by a factor e in 50 swings. The pendu- lum is set into forced vibration by moving its point of suspension horizontally in SHM with an amplitude of 1 mm.

(a) Show that if the horizontal displacement of the pendulum bob is x, and the horizontal displacement of the support is u, the equation of motion of the bob for small oscillations is \(\frac{dx^{2}}{dt^{2}}+\gamma\frac{dx}{dt}+(g/l)x = (g/l) u\) Solve this equation for steady-state motion, if u = u0 cos %u03C9t. (Put %u03C902 = g/l.)

(b) At exact resonance, what is the amplitude of the motion of the pendulum bob? (First, use the given information to find Q.)

Reference no: EM13585357

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