First slide

Simple hormonic motion

Question

In the arrangement shown, the blocks are pulled apart by 3 cm and released. If maximum velocity of 1 kg block is 1 m/s, what is the maximum velocity of 2 kg block?

Moderate

A

0.125 m/s
B

0.25 m/s
C

2 m/s
D

0.5 m/s

Solution

The blocks will oscillate with same angular frequency $ω$ . If amplitudes of oscillation of 2 kg and 1 kg blocks are $A_{1}$ and $A_{2}$ respectively, then
$2 \times A_{1} = 1 \times A_{2}$ as centre of mass of the blocks does not move.
Now $\frac{{(V_{2})}_{\max}}{{(V_{1})}_{\max}} = \frac{ω . A_{2}}{ω . A_{1}} = 2$
$∴ {(V_{1})}_{\max} = \frac{1}{2} \frac{m}{s}$

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