First slide

Simple hormonic motion

Question

A horizontal spring block system of mass M executes simple harmonic motion. When the block is passing through its equilibrium position, an object of mass m is put on it and the two move together. Find the new amplitude

Difficult

A

$\sqrt{\frac{M}{M + m}} A$
B

$\sqrt{\frac{M + m}{M}} A$
C

$\sqrt{\frac{m}{M + m}} A$
D

$\sqrt{\frac{M + m}{m}} A$

Solution

Suppose the velocities in the equilibrium position before and after placing the object m and v and v’, and the amplitudes are A and A’ respectively. By conservation of linear momentum we have
$(M + m) ω' A' = M ω A \Rightarrow \sqrt{M + m} A' = \sqrt{M} A \Rightarrow A' = \sqrt{\frac{M}{M + m}} A$

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