First slide

Simple hormonic motion

Question

Two bodies M and N of equal masses arc suspended from two separate mass less springs of spring constants k₁and k₂respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitudes of M to that of N is

Moderate

A

k₁ / k₂
B

$\sqrt{k_{1} / k_{2}}$
C

k₂ / k₁
D

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

Solution

$a_{1} ω_{1} = a_{2} ω_{2} = v_{max} ω_{1} = \sqrt{(\frac{k_{1}}{m})} and ω_{2} = \sqrt{(\frac{k_{2}}{m})} ∴ \frac{a_{1}}{a_{2}} = \frac{ω_{2}}{ω_{1}} = \sqrt{(\frac{k_{2}}{k_{1}})}$

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