Question

A body makes angular simple harmonic motion of amplitude $\pi /10$ rad and time period 0.05 s. If the body is at a displacement $\theta =\pi /10$ rad at t=0,write the equation giving angular displacement as a function of time.

Answer 1

We know that $\omega =\frac{2\pi }{T}=\frac{2\pi }{0.05}=40\pi$

Let the equation be $\theta ={\theta }_{o}cos(\omega t+\varphi )$

At $t=0$, ${\theta }_o=\theta =\frac{\pi }{10}$

$\frac{\pi }{10}=\frac{\pi }{10}cos\left(\varphi \right)$

$cos\varphi =1$

So $\varphi =0$

So $\theta =\frac{\pi }{10}cos\left(40\pi t\right)$