First slide

Simple hormonic motion

Question

In the arrangement shown, the block is slightly displaced to the right and then released. Then time period of oscillation of the block is

Moderate

A

$2 π \sqrt{\frac{5 m}{3 k}}$
B

$2 π \sqrt{\frac{2 m}{3 k}}$
C

$2 π \sqrt{\frac{3 m}{5 k}}$
D

$2 π \sqrt{\frac{3 m}{k}}$

Solution

(2)
Effective spring constant of the system
$\begin{array}{l} = K + \frac{K (1 \times 1)}{1 + 1} \\ = \frac{3 k}{2} \end{array}$
When the block is displaced slightly ;
$m a = - \frac{3 k}{2} \times x$
$a = - \frac{3 k x}{2 m}$
$c o m p a r i n g w i t h a = - ω^{2} x$
$\begin{array}{l} ω = \sqrt{\frac{3 k}{2 m}} \\ ∴ T = \frac{2 π}{ω} = 2 π \sqrt{\frac{2 m}{3 k}} \end{array}$

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