Question

A simple harmonic motion is represented by
x(t)=cos omega t
Obtain expressions for velocity and acceleration of the oscillator. Also, plot the time variation of displacement, velocity and acceleration of the oscillator.

Answer 1

Answer on Question #65697-Physics-Mechanics

A simple harmonic motion is represented by

$$x (t) = \cos \omega t$$

Obtain expressions for velocity and acceleration of the oscillator. Also, plot the time variation of displacement, velocity and acceleration of the oscillator.

Solution

The velocity is

$$v (t) = \frac {d x}{d t} = - \omega \sin \omega t$$

The acceleration of the oscillator is

$$a (t) = \frac {d v}{d t} = - \omega^ {2} \cos \omega t$$

The plot of the time variation of displacement, velocity and acceleration of the oscillator for $\omega = 1$ :

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