A spring mass system is held at rest with the spring relaxed at a height (H) above the ground. Determine the minimum value of (H) so that the systen has a tendency to rebound after hitting the ground. Given that the coefficient of restitution between `(m_(2))` and ground is zero.
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Explanation

Using energy conservation
`(1)/(2)m_(1)v^(2)=m_(1)gx+(1)/(2)kx^(2)`
Since `v^(2)=2gH` and
For the block `M_(2)` to just lift off,
`x=(m_(2)g)/(K)`, `:. M_(1)gH=m_(1)g((m_(2)g)/(K))+(1)/(2)K((m_(2)g)/(K))^(2)`
or, `H=(m_(2)g)/(K)[(2m_(1)+m_(2))/(2m_(1))]`