An object moving in simple harmonic motion has an amplitude of 0.05 m and a maximum acceleration of 40 m/s².What is the frequency of the system?

Question

An object moving in simple harmonic motion has an amplitude of 0.05 m and a maximum acceleration of 40 m/s².What is the frequency of the system? A) 14.1 Hz B) 177.7 Hz C) 4.5 Hz D) 11.3 Hz E) 2 Hz

Quizplus · Accepted Answer

Maximum acceleration in simple harmonic motion is given by a = ω^2A, where ω is the angular frequency and A is the amplitude.

Rearranging the equation, we get:

ω = √(a/A)

From the given data, maximum acceleration (a) = 40 m/s^2 and amplitude (A) = 0.05 m.

Substituting these values, we get:

ω = √(40/0.05) = 89.44 rad/s

The frequency (f) of the system is given by:

f = ω/2π

Substituting the value of ω, we get:

f = 89.44/2π ≈ 14.1 Hz

Therefore, the answer is C) 4.5 Hz.

An Object Moving in Simple Harmonic Motion Has an Amplitude