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

Conservation of mechanical energy give,
`E_(A)=E_(B)`
or `1/2m_(1)v^(2) =1/2kx^(2)+m_(1)gx`
or `2m_(1)gH=kx^(2) +2m_(1)gx`

the lower block will rebounce when
`xgt(m_(2)g)/k ,(kx=m_(2)g)`
Substituting, `x=(m_(2)g)/k` in Eq. (i), we get
`2m_(1) gH=k((m_(2)g)/(k))^(2) +2m_(1)g((m_(2)g)/(k))`
or `H=(m_(2)h)/k((m_(2)+2m_(1))/(2m_(1)))`
Thus, `H_("min")=(m_(2)g)/(k)((m_(2) +2m_(1))/(2m_(1))a)`