First slide

Simple harmonic motion

Question

What is the maximum acceleration of the particle doing the SHM $y = 2 \sin [\frac{πt}{2} + φ]$ where 2 is in cm

Moderate

A

$\frac{π}{2} cm / s^{2}$
B

$\frac{π^{2}}{2} cm / s^{2}$
C

$\frac{π}{4} cm / s^{2}$
D

$= \frac{π^{2}}{8} cm / s^{2}$

Solution

Comparing given equation with standard equation,
$y = A \sin (ωt + φ),$ we get, $A = 2 cm,$ $ω = \frac{π}{2}$
$∴ a_{\max} = ω^{2} A$ $= {(\frac{π}{2})}^{2} \times 2$ $= \frac{π^{2}}{2} cm / s^{2}$

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