In a simple harmonic oscillator, if the maximum speed is 4 m/s and the amplitude

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Question: In a simple harmonic oscillator, if the maximum speed is 4 m/s and the amplitude is 2 m, what is the angular frequency?

Options:

Correct Answer: 4 rad/s

Solution:

Maximum speed (v_max) = ωA. Thus, ω = v_max/A = 4/2 = 2 rad/s.

In a simple harmonic oscillator, if the maximum speed is 4 m/s and the amplitude is 2 m, what is the angular frequency?

In a simple harmonic oscillator, if the maximum speed is 4 m/s and the amplitude is 2 m, what is the angular frequency?

Step 1: Identify the maximum speed (v_max) given in the problem, which is 4 m/s.
Step 2: Identify the amplitude (A) given in the problem, which is 2 m.
Step 3: Recall the formula for maximum speed in a simple harmonic oscillator, which is v_max = ωA, where ω is the angular frequency.
Step 4: Rearrange the formula to solve for angular frequency (ω): ω = v_max / A.
Step 5: Substitute the values into the formula: ω = 4 m/s / 2 m.
Step 6: Calculate the result: ω = 2 rad/s.

Simple Harmonic Motion – The motion of an object where the restoring force is directly proportional to the displacement from equilibrium, characterized by parameters such as amplitude, angular frequency, and maximum speed.
Angular Frequency – A measure of how quickly an object oscillates in simple harmonic motion, calculated using the formula ω = v_max / A.