Question

What is the maximum acceleration of the particle doing the SHM?
$y=2\sin \left[\frac{\pi t}{2}+\varphi \right]$ , where $2$ is in cm

• A. $\frac{\pi }{2}cm/s^2$
• B. $\frac{{\pi }^2}{2}cm/s^2$
• C. $\frac{\pi }{4}cm/s^2$
• D. $\frac{{\pi }^2}{4}cm/s^2$

Answer 1

Answer: (B)

$y=2\sin \left[\frac{\pi t}{2}+\varphi \right]$,
where $2$ is in $cm$
Compare the equation with the standard equation,
$A=\sin (wt+\varphi )$
$\Rightarrow A=2cm,$
$w=\frac{\pi }{2}$
Acceleration of the particle is
$a=w^{2}x$
At $x=+A,a=a_{\max }$
$\therefore a_{\max }=w^{2}A=\frac{{\pi }^2}{2}cm/s^2$