First slide

Simple hormonic motion

Question

A block of mass m is at rest on an another block of same mass as shown in figure. Lower block is attached to the spring then the maximum amplitude of motion so that both the block will remain in contact is

Moderate

A

$\frac{mg}{2 k}$
B

$\frac{mg}{k}$
C

$\frac{2 mg}{k}$
D

$\frac{3 mg}{2 k}$

Solution

The blocks will remain in contact till the blocks do not go above the natural length of the spring, because after this condition the deceleration of lower block becomes more then upper block due to spring force. So they will get separated.
So maximum possible amplitude = $x_{0} = \frac{2 mg}{k}$

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