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How to better understand a SHM graph
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Lets start with first defining simple harmonic motion, what is SHM?
Next we have the frequency, how is this determined?
A simple harmonic motion is a continuous motion of a uniform oscillation that keeps on oscillating at a constant rate up and down through the equilibrium
The frequency of a SHM graph is the "number of oscillations per second."
- The frequency of an oscillation is simply determined by dividing 1 by the time period
- F=1/T (units are in Hertz(HZ))
- For example: If the time period of an oscillation is 4 seconds what is the frequency?
- F=1/4 seconds
F=0.25Hz
Some examples include:
- A simple pendulum
- A car tire traveling at at constant speed
- A vertical oscillation with no resistance
Ryan Sangha
January 25, 2014
Simple Harmonic Motion
How to better understand the kinematics of a SHM graph
How is the amplitude of an oscillation measured on a SHM graph?
What is the time period of SHM graph?
- The amplitude of the oscillation is measured from the equilibrium point to either the crest or the trough of the graph.
Amplitude measurement:
- The time period of a SHM graph is the time that the oscillation takes to complete one full cycle.
- There are two ways of measuring one full cycle, either the time period of the oscillation from crest to crest or trough to trough or by the example below.
Example of determining the amplitude:
- The Amplitude of this graph is determined by subtracting two values, (The highest/lowest vertical point) - (Equilibrium point)
- This Amplitude is therefor (10.0cm)-(0cm) which is 10cm.
Now you may be asking, what is the other way to measure one full cycle?
Example:
Illustrated on diagram
Lastly, we have phase constant, what is a phase constant, and how is it determined?
- Phase constant is the initial angle at which time is zero.
- Phase is determined by: phi
x(0)=Acos(phi)
x(0) is displacement at time=0
A is amplitude
phi=cos^-1(x(0)/A)
Example:
x(0)=0cm
A=10cm
phi=cos^-1(0/10)
phi=cos^-1(o)
phi= pi/2 or 3pi/2
Now you may be wondering which one is the correct phase constant, it will be 3pi/2 because the graph slopes upwards to start and a cosine wave that slopes up is at the point 3pi/2