Two particles performing simple harmonic motions of maximum accelerations, 1 m/s 2 and 100 m/s 2 , have the same amplitudes. The ratio of their angular frequencies is

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The maximum acceleration of a particle in simple harmonic motion is given by $a_{m a x} = ω^{2} A$ , where $ω$ is the angular frequency and $A$ is the amplitude.

For the first particle, $a_{1} = ω_{1}^{2} A = 1$ .

For the second particle, $a_{2} = ω_{2}^{2} A = 100$ .

Taking the ratio of the two maximum accelerations:

$\frac{a _{1}}{a _{2}} = \frac{ω _{1}^{2} A}{ω _{2}^{2} A} = \frac{1}{100}$

$\frac{ω _{1}^{2}}{ω _{2}^{2}} = \frac{1}{100}$

$\frac{ω _{1}}{ω _{2}} = \frac{1}{10}$

The ratio of their angular frequencies is $1 : 10$ .

Answer: $1 : 10$

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