Investigation of Simple Harmonic Motion There are two common forms of the equations used to model simple harmonic motion (SHM), which is the motion of springs, swings, tides, and many
other periodic phenomena. These equations are y(t) = A sin(wt +) and y(t) = c2sin wt - acos wt, where:
y() = distance of weight from equilibrium position
w = angular frequency (measured in radians per second)
A = amplitude
$ = phase (depends on initial conditions)
C1 = Asing
2 = Acos
Suppose you are an engineer trying to recreate an experiment involving a weight on the end of a spring. This simulation will give you an idea of
what the experiment will look like. For more information, you can visit this simple harmonic motion website,
You are given the equation y(t) = 2 sin 45t -- 5 cos 4rt, which models the position of the weight, with respect to time. You need to find the
amplitude of the oscillation, the angular frequency, and the initial conditions of the motion. You will also be required to find the times) at which the
weight is at a particular position. To find this information, you need to convert the equation to the first form, y(t) = A sin(wt + )