# Applications of SHM

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Question

# Figure shows a block of mass m = 2 kg resting on a smooth horizontal ground attached to one end of a spring of force constant k =100 N/m in natural length. If another block of same mass and moving with a velocity u = 5 m/s toward right is placed on the block which stick to it due to friction. Find the amplitude of oscillations (in m) of the combined mass 2m.

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Solution

## When second mass sticks to the lower mass, due to such an inelastic collision, the velocity of combined block is reduced by half that is u/2 to conserve momentum. Now at mean position the velocity of block can be written as$\frac{\mathrm{u}}{2}=\mathrm{A\omega }$ [If A is the amplitude of oscillation]or $\frac{\mathrm{u}}{2}=\mathrm{A}\sqrt{\frac{\mathrm{k}}{2\mathrm{m}}}$ [As here for combined block new angular frequency of SHM is $\mathrm{\omega }=\sqrt{\frac{\mathrm{k}}{2\mathrm{m}}}$]or

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