Question

Which of the following properties of a mass-on-a-spring system undergoing simple harmonic motion can be changed without affecting the frequency of oscillation?

Amplitude
Spring stillness
Oscillating mass

Answer 1

Answer: Amplitude

If we are talking about simple harmonic motion, we are talking about waves and in this case the frequency
`f` is related to the period of oscillation
`T` in an inverse proportion.

Now, for a mass-on-a-spring system the period is given by:

`T=2\pi\sqrt{(m)/(k)}`

Where
`m` is the oscillating mass and
`k` the spring constant, which depends on the spring stillness.

As we can see in this equation:

If we change
`m` and
`k` we will affect the period, hence the frequency.

Nevertheless, we do not see any relation with the Amplitude, this means the period (hence the frequency) does not depend on the amplitude.