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Chapter 13: Problem 5

When in its cycle is the acceleration of an undamped simple harmonic oscillator zero? When is the velocity zero?

Short Answer

Expert verified
The acceleration of an undamped simple harmonic oscillator is zero when the oscillator is at the equilibrium point, where it has maximum velocity. The velocity is zero when the displacement is at its maximum value (Amplitude); that is, at the crest and trough of the cycle, where the oscillator is momentarily at rest.

Step by step solution

01

Identify when acceleration is zero

The acceleration is given by \( a = - \omega^2 x \). Acceleration is zero when displacement x is zero. So, the acceleration of the harmonic oscillator is zero at the maximum and minimum points in its cycle, which is when it crosses the equilibrium point.
02

Identify when velocity is zero

The velocity is given by \( v = \omega \sqrt{(A^2 - x^2)} \). Velocity is zero when displacement x equals to the amplitude A. This occurs at the maximum and minimum displacement, i.e. at the extreme points of the oscillation.

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