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Two simple harmonic motions of angular frequency 100 rad s⁻¹ and 1000 rad s⁻¹ have the same displacement amplitude. The ratio of their maximum accelerations is

Asked in CBSE AIPMT 2008 · v-x and a-x relations

Answer: (4) 1:10²

Step-by-step solution

Given: ω₁=100 rad s⁻¹, ω₂=1000 rad s⁻¹, with the same amplitude A.

Idea: the maximum acceleration of SHM is Aω², so equal amplitudes make the ratio depend on ω² alone.

(a₁)/(a₂)=(Aω₁²)/(Aω₂²)=((100)/(1000))²

=(1/(10))²=1/(100)

So the ratio is 1:10².

Why the other options are wrong

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