The equation of motion of a one-dimensional simple harmonic oscillator is
x(t) = Acos(wt+f)
where A is the amplitude, omega is the angular frequency, and phi is the phase.
What are the equations for velocity and acceleration as a function of time?
From these equations, write equations for the maximum speed (i.e. amplitude of the velocity vs. time function) and the maximum acceleration (i.e. amplitude of the acceleration vs. time function).
Verify the correctness of these equations for the maximum speed and maximum acceleration by measuring the angular frequency of the oscillator and the amplitude of the oscillator, calculating the maximum speed and acceleration, and comparing these values to those found on the graphs.
Compare the position, velocity, and acceleration graphs below. When the position is a maximum, what are the velocity and acceleration?
When the position of the oscillator is at its equilibrium point, what are the velocity and acceleration?
When the position of the oscillator is at a minimum, what are the velocity and acceleration?