How do you find the amplitude, period, vertical and phase shift and graph #y=cos(theta+pi/3)#?

1 Answer
May 15, 2018

Simple Harmonic Motion/Oscillations (SHM) are graphed with cosine or sine functions, and the amplitude; period and phase shift can easily be found in the following way:

The graph for displacement can be described with:

#Acos(theta + phi)#
Given: #theta = theta_{i} + omega t #
The angular displacement is equal to the angular velocity * time.
We can substitute this into our equation:

#Acos(omega * t + phi)#

Where:
A == Amplitude
#omega# == Angular Velocity
#t# == time
#phi# == phase change

In your example:
#y = Acos(omega * t + pi/3)#

The Amplitude is equal to 1 (same as #1cos(omega*t + phi)#)
The Phase Change (#phi#) is equal to #pi/3#

We know the period (T) is equal to:

#T = (2pi) / omega#
#omega = (2pi) / T#

Hence, substituting you will get
#y = Acos((2pi) / T * t + pi/3)#

To find the period we will have to substitute a value for time or find a time for displacement = 0