Question 205: Oscillations

Question

A mass $$0.9 \mathrm{~kg}$$, attached to a horizontal spring, executes SHM with an amplitude $$\mathrm{A}_{1}$$. When this mass passes through its mean position, then a smaller mass of $$124 \mathrm{~g}$$ is placed over it and both masses move together with amplitude $$A_{2}$$. If the ratio $$\frac{A_{1}}{A_{2}}$$ is $$\frac{\alpha}{\alpha-1}$$, then the value of $$\alpha$$ will be ___________.

Accepted Answer

$$(0.9){A_1}\sqrt {{K \over {0.9}}}  = (0.9 + 0.124){A_2}\sqrt {{K \over {0.9 + 0.124}}} $$
$${{{A_1}} \over {{A_2}}} = \sqrt {{{0.9 + 0.124} \over {0.9}}} $$
$$ = \sqrt {{{1.024} \over {0.9}}} $$
$$ = {\alpha  \over {\alpha  - 1}}$$
$$\alpha  = 16$$

Oscillations

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