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A block of mass m is attached to two uns...

A block of mass m is attached to two unstretched springs of spring constant `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 a distance `x//4` from its mean position. All the surfaces are smooth.

Text Solution

Verified by Experts

Applying conservation of energy
`1/2k_(1)x^(2)+1/2 k_(2)x^(2)=1/2 mv^(2)+1/2 k_(1)(x//4)^(2)+1/2 k_(2)(x//4)^(2)`
`v=(x)/(4m) sqrt(15(k_(1)+k_(2)))`.
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