# Amplitude dependencies in an oscillator

• malignant
In summary: Well, when the stone leaves the box, the system gains kinetic energy. This increases the amplitude, because the system is now vibrating at a higher frequency.
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.

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.

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

malignant said:
Maybe I'm getting SHM mixed up with simple pendulums.

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.

malignant said:
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.

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

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

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?

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?

## 1. What is an oscillator?

An oscillator is a device or system that produces a periodic, repeating waveform or signal. This can take the form of mechanical, electrical, or other types of oscillation.

## 2. What is amplitude in relation to an oscillator?

Amplitude is the maximum displacement or distance from the equilibrium position of an oscillating system. In other words, it is the magnitude or strength of the oscillation.

## 3. How does amplitude affect the behavior of an oscillator?

The amplitude of an oscillator directly affects its frequency and period. As the amplitude increases, the frequency also increases, and the period decreases. This means that the oscillator will complete more cycles in a given amount of time.

## 4. What are the amplitude dependencies in an oscillator?

Amplitude dependencies in an oscillator refer to the relationship between the amplitude and other parameters such as frequency, period, and energy. This relationship can vary depending on the type of oscillator and the specific properties of the system.

## 5. How can amplitude dependencies be manipulated in an oscillator?

Amplitude dependencies can be manipulated by adjusting the parameters of the oscillator, such as the spring constant, mass, or damping coefficient. Additionally, external forces or inputs can also affect the amplitude dependencies of an oscillator.

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