First slide

Simple harmonic motion

Question

The motion of a particle varies with time according to the relation $y = a (sinω t + cosω t)$ , then

Moderate

A

The motion is oscillatory but not S.H.M.
B

The motion is S.H.M. with amplitude a
C

The motion is S.H.M. with amplitude $a \sqrt{2}$
D

The motion is S.H.M. with amplitude 2a

Solution

$y = a (cosω t + sinω t) = a \sqrt{2} [\frac{1}{\sqrt{2}} cosω t + \frac{1}{\sqrt{2}} sinω t]$
$= a \sqrt{2} [\sin 45 ° cosω t + \cos 45 ° sinω t]$
$= a \sqrt{2} \sin (ω t + 45 °) \Rightarrow$ Amplitude $= a \sqrt{2}$

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