1. Tardigrade
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  3. Physics
  4. A 1 kg block is executing simple harmonic motion of amplitude 0.1 m on a smooth horizontal surface under the restoring force of a spring of spring constant 100 N / m A block of mass 3 kg is gently placed on it at the instant it passes through the mean position. Assuming that the two blocks move together, the amplitude of the motion is

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Q. A 1 kg block is executing simple harmonic motion of amplitude 0.1 m on a smooth horizontal surface under the restoring force of a spring of spring constant 100 N / m A block of mass 3 kg is gently placed on it at the instant it passes through the mean position. Assuming that the two blocks move together, the amplitude of the motion is

Oscillations

Solution:

At mean position, the speed gets altered by conservation of momentum, $(1\, kg )\left(v_{1}\right)=(1+3) kg \left(v_{2}\right)$
$v_{2}=\frac{v_{1}}{4}$ Now, $\frac{1}{2}(1 \,kg ) v_{1}^{2}=\frac{1}{2} k A^{2}\, \dots (i)$
$\frac{1}{2}(4 \,kg ) v_{2}^{2}=\frac{1}{2} K A^{2}\, \dots (ii) $
Dividing (ii) by (i), we get
$\frac{4 v_{2}^{2}}{v_{1}^{2}}=\left(\frac{A^{\prime}}{A}\right)^{2}\, \dots (ii)$
$\frac{2 v_{2}}{v_{1}}=\frac{A^{\prime}}{A} \Rightarrow \frac{A^{\prime}}{A}=2\left(\frac{1}{4}\right)=\frac{1}{2}$
$\Rightarrow A^{\prime}=\frac{A}{2}=\frac{10 \,cm }{2}=5 \,cm$