Question

A simple harmonic motion is represented by x(t)=acos wt 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 Question #65632 – Physics – Mechanics – Relativity

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

Solution. Consider the equation $x(t) = a \cos wt$ , where $a$ is the amplitude of the oscillation (maximum displacement), $w$ – the angular frequency, $t$ – time.

The velocity of the object as a function of time is given by

$$v (t) = \frac {d x (t)}{d t} = a (- \sin w t) w = - a w \sin w t.$$

and the acceleration is given by

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

Plot the time variation of displacement, velocity and acceleration of the oscillator.

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