Question

A block of mass m is attched to two unstretched springs of spring constants $k_1$ and $k_2$ as shown in figure (8-E9). The block is displaced towards right through a distance x and is released. Find the speed of the block as it passes through the mean position shown.

Answer 1

The body is displaced x towards right,

Let the velocity of the body be v at its mean position,

Applying law of conservation of energy

$\frac{1}{2}m{v}^2=\frac{1}{2}{k}_1{x}^2+\frac{1}{2}{k}_2{x}^2$

$\Rightarrow m{v}^2=x^2(k_1+k_2)$

$\Rightarrow v^2=\frac{x^2(k_1+k_2}{m}$

$\Rightarrow v=x\sqrt{\frac{k_1+k_2}{m}}$