First slide

Simple hormonic motion

Question

A block of mass m is attached to two unstretched springs of spring constants k, each as shown. The block is displaced towards right through a distance x and is released. The speed of the block as it passes through the mean position will be

Moderate

A

$x \sqrt{\frac{m}{2 k}}$
B

$x \sqrt{\frac{2 k}{m}}$
C

$x \sqrt{\frac{m}{k}}$
D

$x \frac{2 k}{m}$

Solution

Total PE of spring = Total KE of block
$\frac{1}{2} k x^{2} + \frac{1}{2} k x^{2} = \frac{1}{2} m v^{2} \Rightarrow k x^{2} = \frac{1}{2} m v^{2}$
$\Rightarrow$ Speed of the block, $v = x \sqrt{\frac{2 k}{m}}$

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