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 passes through the mean position shown.

Options

A. `sqrt((k_(1)+k_(2))/m) x`
B. `sqrt((k_(1)k_(2))/(m(k_(1)+k_(2))))x`
C. `sqrt((k_(1)^(2)k_(2)^(2))/(m(k_(1)^(2)+k_(2)^(2))))x`
D. `sqrt((k_(1)^(3)k_(2)^(3))/(m(k_(1)^(3)+k_(2)^(3))))`

Answer

A

Explanation

`1/2 K_(2)x^(2)+1/2 K_(1)x^(2)=1/2 m v^(2)`
`v=sqrt((K_(1)+K_(2))/m) x`