Question

The equation of a particle executing SHM is $x=\left(5m\right)\sin \left[\right(\pi s^{-1}t=\frac{\pi }{6}]$. Write down the amplitude, initial phase constant, time period and maximum speed.

Answer 1

The general equation of SHM is
$x=ASin(\omega t+\varphi )$

where $A$ is the amplitude
$\omega$ is the angular frequency
$\varphi$ is the initial phase constant

Here

$x=\left(5m\right)Sin(\pi s^{-1}t+\frac{\pi }{6})$

a) $A$ =Amplitude = $5m$

b) $\varphi$ = Initial phase constant = $\frac{\pi }{6}$

c) Angular frequency, $\omega =\pi rad/sec$

$\therefore$ Time period, $T=\frac{2\pi }{\omega }=\frac{2\pi }{\pi }=2sec$

d) Maximum Speed, $v_{max}=|A\omega |=|5\times 2|=10m/sec$