How is the amplitude of a simple harmonic oscillator determined?

The amplitude of a simple harmonic oscillator is determined by the maximum displacement from equilibrium.

A simple harmonic oscillator is a system that oscillates back and forth around an equilibrium position with a constant frequency. The amplitude of the oscillator is the maximum displacement from equilibrium. It is determined by the initial conditions of the system, such as the initial displacement and velocity.

For example, consider a mass attached to a spring that is oscillating back and forth. The displacement of the mass from equilibrium can be described by the equation:

x(t) = A cos(ωt + φ)

where A is the amplitude, ω is the angular frequency, t is time, and φ is the phase angle. The angular frequency is determined by the mass and spring constant:

ω = √(k/m)

where k is the spring constant and m is the mass.

To determine the amplitude of the oscillator, we need to know the initial conditions. For example, if the mass is initially displaced by a distance of x0 and released from rest, then the amplitude is:

A = x0

If the mass is given an initial velocity of v0 and released from the equilibrium position, then the amplitude is:

A = v0/ω

In summary, the amplitude of a simple harmonic oscillator is determined by the maximum displacement from equilibrium, which is determined by the initial conditions of the system.