Question

A mass 0.9 kg, attached a horizontal spring, executes SHM with an amplitude A1. When this mass passes through its mean position, then a smaller mass of 124 g is placed over it and both masses move together with amplitude A2. If the ratio A1/A2 is α/(α - 1), then the value of α will be _____.

Answer 1

The correct answer is 16
$(0.9)A_1\sqrt{\frac{K}{0.9}}=(0.9+0.124)A_2\sqrt{\frac{K}{0.9+0.124}}$
$\frac{A_1}{A_2}=\sqrt{\frac{0.9+0.124}{0.9}}$
$=\sqrt{\frac{1.024}{0.9}}$
$=\frac{α}{α−1}= α=16$
$\therefore$ the value of α will be 16