# Amplitude dependencies in an oscillator

1. Feb 21, 2014

### malignant

I know amplitude doesn't depend on mass but I came across a problem where the amplitude changed with a change in mass.

The problem was a horizontal frictionless spring with a box of mass m1 attached to it with a stone of mass m2 inside of the box. At its equilibrium point at its maximum speed, the stone left the box and the amplitude got smaller.

I'm confused as to why it changed? I can post the problem if it's not enough information.

2. Feb 22, 2014

### dauto

What do you mean by the amplitude doesn't depend on the mass?
Look at the formula for the angular frequency

$$\omega = \sqrt{\frac{k}{m}},$$

and look at the relationship between the maximum speed and the amplitude

$$v_{MAX}=\omega A$$

If the mass changes but the maximum speed doesn't, than the amplitude must change.

3. Feb 22, 2014

### malignant

What about initially? Like not changing mass but different initial mass. Maybe I'm getting SHM mixed up with simple pendulums.

4. Feb 22, 2014

### AlephZero

For simple harmonic motion of a "mass on a spring", the force only depends on the change in length of the spring. The same force applied to a larger mass produces a smaller acceleration, and a lower oscillation frequency.

For a pendulum, the force also depends on the weight, which is of course proportional to the mass. So the acceleration of the mass, and the oscillation frequency of the pendulum, is independent of the mass.

5. Feb 22, 2014

### sophiecentaur

Clue: How does the energy in the oscillating system change when the stone leaves the box?

6. Feb 22, 2014

### malignant

I think I see now. If the stone left the box when it was fully extended and there's no kinetic energy, then there isn't a mass variable, so would the amplitude not change then?

7. Feb 23, 2014

### sophiecentaur

The box is in at the position of maximum extension so why would the amplitude of the oscillations change? The stone has 'taken' no energy from the system. So what actually will change?