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Chapter 13: Problem 5

How does the frequency of a simple harmonic oscillator depend on its amplitude?

Short Answer

Expert verified
The frequency of a simple harmonic oscillator is independent of its amplitude. Therefore, no matter how big or small the amplitude is, the frequency remains unchanged.

Step by step solution

01

Understand the underlying Physics

A simple harmonic oscillator is a type of periodic motion where the restoring force is directly proportional to the displacement. Examples include a swinging pendulum or a mass on a spring. The frequency is given as \(f = \frac{1}{T}\), where T is the time period of one complete oscillation, dictated by the properties of the oscillator and not influenced by the amplitude or the displacement from the equilibrium position.
02

Consider amplitude's impact

Amplitude is the oscillator's maximum displacement from the equilibrium position. While it dictates the 'size' of the oscillations, for simple harmonic motion, it does not influence the time it takes for one complete oscillation nor the frequency.
03

Formulate relationship

Since neither the time period T nor the frequency f is influenced by amplitude in simple harmonic motion, we can state that the frequency of a simple harmonic oscillator does not depend on its amplitude.

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Most popular questions from this chapter

If the spring of a simple harmonic oscillator is cut in half, what happens to the frequency?

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