First slide

Simple harmonic motion

Question

Identify the correct statements for an SHM with amplitude A and maximum velocity = V
(i)At position x = $\frac{A}{2}$ , velocity lags displacement by $\frac{π}{2}$
(ii)At position x = $\frac{A}{\sqrt{2}}$ , velocity leads displacement by $\frac{π}{4}$
(iii)When velocity = $\frac{V}{\sqrt{2}}$ , acceleration leads velocity by $π$
(iv)When velocity = $- \frac{V}{\sqrt{2}}$ , acceleration leads velocity by $\frac{π}{2}$

Easy

A

(i) only
B

(iii) only
C

(i) and (iii) only
D

(iv) only

Solution

In SHM, $y = A \sin ω t ∴ Velocity, v = A ω \cos ω t = A ω \sin (ω t + \frac{π}{2})$
and acceleration, $a = - A ω^{2} \sin ω t = A ω^{2} \sin (ω t + π)$
Velocity leads displacement by $\frac{π}{2}$ , acceleration leads velocity by $\frac{π}{2}$ .

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App