First slide

Applications of SHM

Question

Two equal masses are suspended separately by two springs of constants k₁ and k₂. If their oscillations satisfy the condition that their maximum velocities are equal, then the ratio of the amplitudes of the oscillations of the masses respectively is

Moderate

A

$\frac{k_{1}}{k_{2}}$
B

$\frac{k_{2}}{k_{1}}$
C

$\sqrt{\frac{k_{1}}{k_{2}}}$
D

$\sqrt{\frac{k_{2}}{k_{1}}}$

Solution

Maximum velocity ( $ω$ A) are equal:
$\begin{array}{l} ω_{1} A_{1} = ω_{2} A_{2} \\ \Rightarrow \frac{A_{1}}{A_{2}} = \frac{ω_{2}}{ω_{1}} = \sqrt{\frac{k_{2}}{k_{1}}} (∵ ω = \sqrt{k / m}) \end{array}$

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