Question

The amplitude of oscillation is the maximum distance between the oscillating weight and the equilibrium position. Determine the frequency of oscillation for several different amplitudes by pulling the weight down different amounts while still keeping the simulation within the top and botom boundaries. How does the frequency depend on the amplitude of oscillation

Answer 1

In no case does the amplitude appear, so we would not have to change the period of the system when we change to the amplitude

Step-by-step explanation:

In the harmonic movement when the amplitude of oscillation increases, body speed also increases, so the frequency remains constant.

When we solve the different case of harmonic movement

Simple pendulum 2pi f = Ra l / g

Spring mass 2pi f = RA k / m

2pi torsion pendulum f = RA I / k

In no case does the amplitude appear, so we would not have to change the period of the system when we change to the amplitude

Answer 2

The frequency does not depend on the amplitude for any (ideal) mechanical or electromagnetic waves.

In electromagnetism we have that the relation is:

Velocity = wavelenght*frequency.

So the amplitude of the wave does not have any effect here.

For a mechanical system like an harmonic oscillator (that can be used to describe almost any oscillating system), we have that the frequency is:

f = (1/2*pi)*√(k/m)

Where m is the mass and k is the constant of the spring, again, you can see that the frequency only depends on the physical properties of the system, and no in how much you displace it from the equilibrium position.

This happens because as more you displace the mass from the equilibrium position, more will be the force acting on the mass, so while the "path" that the mass has to travel is bigger, the mas moves faster, so the frequency remains unaffected.