First slide

Simple hormonic motion

Question

A particle is executing a simple harmonic motion. Its maximum acceleration is $α$ and maximum velocity is $β$ . Then, its time period of vibration will be

Easy

A

$\frac{β^{2}}{α}$
B

$\frac{2 π β}{α}$
C

$\frac{β^{2}}{α^{2}}$
D

$\frac{α}{β}$

Solution

If A and $ω$ be amplitude and angular frequency of vibration, then
$α = ω^{2} A$ . . . . (i)
$and β = ω A$ . . . . .(ii)
Diving eqn. (i) by eqn. (ii), we get
$\frac{α}{β} = \frac{ω^{2} A}{ω A} = ω$
$∴ Time period of vibration is$
$T = \frac{2 π}{ω} = \frac{2 π}{(α / β)} = \frac{2 π β}{α}$

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