Question

Give an example of a simple harmonic oscillator, specifically noting how its frequency is independent of amplitude.

Short answer

A mass attached to a spring on a frictionless surface.

Step-by-step solution

Definition of simple harmonic motion 

Simple Harmonic Motion is a kind of periodic motion where the body oscillates to and from about the equilibrium positionsuch that the maximum displacement of the body on either side is the same.

The force acting on the body during motion is always directed toward the center and is proportional to its displacement.

Relationship between frequency and amplitude

When a mass attached to a spring system oscillate about its equilibrium point, therestoring force exerted upon the spring is measured such that the force F always acts towards the equilibrium point and is expressed as follows,

\(F = - kx\)

Here, K is the spring constant which is related to the stiffness of the spring. A stiff spring would have a high spring constant and is the amount the spring stretches relative to its equilibrium position.

Write the expression for the frequency for the simple harmonic motion.

\(f = \frac{1}{{2\pi }}\sqrt {\left( {\frac{k}{m}} \right)} \)

Here, k is the spring constant and m is the mass of a system.

It is observed that the frequency does not depend on the amplitude of oscillation but on spring constant and mass.

Thus, the frequency is independent of amplitude.