One end of a spring of force constant k is fixed to a vertical wall and the other to a block of mass m resting on a smooth horizontal surface. There is another wall at a distance ${x_0}$ from the black. The spring is then compressed by $2{x_0}$ and released. The time taken to strike the wall is
Diffcult
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(c) The total time from $A$ to $C$
${t_{Ac}} = {t_{AB}} + {t_{BC}}$
$ = (T/4) + {t_{BC}}$
where $T =$ time period of oscillation of spring mass system
${t_{BC}}$ can be obtained from, $BC = AB\sin (2\pi /T)\,{t_{BC}}$
Putting $\frac{{BC}}{{AB}} = \frac{1}{2}$ we obtain ${t_{BC}} = \frac{T}{{12}}$
==> ${t_{AC}} = \frac{T}{4} + \frac{T}{{12}} = \frac{{2\pi }}{3}\sqrt {\frac{m}{k}} $.
${t_{Ac}} = {t_{AB}} + {t_{BC}}$
$ = (T/4) + {t_{BC}}$
where $T =$ time period of oscillation of spring mass system
${t_{BC}}$ can be obtained from, $BC = AB\sin (2\pi /T)\,{t_{BC}}$
Putting $\frac{{BC}}{{AB}} = \frac{1}{2}$ we obtain ${t_{BC}} = \frac{T}{{12}}$
==> ${t_{AC}} = \frac{T}{4} + \frac{T}{{12}} = \frac{{2\pi }}{3}\sqrt {\frac{m}{k}} $.
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