Given the Graph on Simple Harmonic Motion: Using the information from the graph,

Question

Given the Graph on Simple Harmonic Motion:

Using the information from the graph, find:

a) amplitude

b) angular frequency

c) phase shift in units of seconds, needed to write the displacement as a cosine function

d) phase shift in units of radians, needed to write the displacement as a cosine function

e) phase shift in units of seconds, needed to write the displacement as a sine function

f) phase shift in units of radians, needed to write the displacement as a sine function

g) Using these specific values, write a cosine function (using the general form above) for this motion. (That is, it should have the form of the above equations with A, ?, and ? replaced with numbers.)

h) Using these specific values, write a sine function (using the general form above) for this motion.

i) Use your cosine equation to calculate the displacement at time 6.8s

j) Use your sine equation to calculate the displacement at time 6.8s

k) Starting from your cosine function produce an equation for the velocity of this motion.

l) Starting from your sine function produce an equation for the velocity of this motion.

Explanation / Answer

a)
AMplitude = maximum displacement
= 3 m
b)
time period = 4.5 s
angular frequency = 2*pi/T
= 2*pi/4.5
= 1.4 rad/s
c)
shift needed = 0.8 s
d)
4.5 s = 2*pi rad
0.8 s = (2*pi*0.8)/4.5
= 1.12 rad

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