The maximum speed of a simple harmonic oscillator is 4 m/s. If the amplitude is

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Question: The maximum speed of a simple harmonic oscillator is 4 m/s. If the amplitude is 2 m, what is the angular frequency? (2019)

Options:

Correct Answer: 4 rad/s

Exam Year: 2019

Solution:

Maximum speed (v_max) = ωA => ω = v_max / A = 4 m/s / 2 m = 2 rad/s.

The maximum speed of a simple harmonic oscillator is 4 m/s. If the amplitude is 2 m, what is the angular frequency? (2019)

The maximum speed of a simple harmonic oscillator is 4 m/s. If the amplitude is 2 m, what is the angular frequency? (2019)

Step 1: Understand the terms. The maximum speed (v_max) of the oscillator is given as 4 m/s, and the amplitude (A) is given as 2 m.
Step 2: Recall the formula that relates maximum speed, angular frequency (ω), and amplitude: v_max = ωA.
Step 3: Rearrange the formula to solve for angular frequency (ω): ω = v_max / A.
Step 4: Substitute the values into the formula: ω = 4 m/s / 2 m.
Step 5: Perform the division: 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.
Maximum Speed – The highest speed reached by an object in simple harmonic motion, occurring as it passes through the equilibrium position.