Question

A block of mass m is attached to two unstretched springs of spring constants `k_1 and k_2` as shown in figure. The block is displaced towards right through a distance x and is released. Find the speed of the block as it psses through the mean position shown.

Answer 1

Correct Answer - A::B
The body is displayed x towards righ.
Let the velocity of the body be v at its mean position.
Applying law of conservation of energy
`1/2 mv^2=1/2k_1x^2+1/2k_2x^2`

`rarr mv^2=x^2(k_1+k_2)`
`rarr v^2=(x^2(k_1+k_2)/m`
`rarr v=xsqrt((k_1+k_2)/m)`