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

Options

(a) 1 : 10
(b) 1 : 10²
(c) 1 : 10³
(d) 1 : 10⁴

Correct Answer:

1 : 10²

Explanation:

Maximum acceleration of a particle in the simple harmonic motion is directly proportional to the square of angular frequency i.e., a(max)= – w ² A

As A remains same, we can say
a₁ / a₂ = w₁² / w₂² =  (100)² / (1000)² = 1 / 100
⇒ a₁ : a₂ = 1 : 10²