College Physics : Harmonic Motion
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Example Questions
Example Question #1 : Harmonic Motion
A pendulum is made up of a small 
The angular frequency of a simple pendulum is 
Example Question #2 : Motion
Which of the following is not an example of simple harmonic motion?
A child swinging on a swing set
The mass on a pendulum moving back and forth
A plucked string vibrating on a guitar
A book falling to the ground
A book falling to the ground
For this question, we need to recall what simple harmonic motion is. Remember that it is a periodic motion where the restoring force depends on the displacement of the object undergoing these motions. So to answer this question, we need to keep this idea in mind and see which example doesn't match up.
A mass on a pendulum moving back and forth is clearly an example of simple harmonic motion. As the mass moves further from the center in either direction, it experiences a greater and greater force in the opposite direction.
A child swinging on a swing set is another correct example. This situation is analogous to the mass on a pendulum swinging back and forth.
A vibrating guitar string is yet another example of simple harmonic motion. After it is plucked, the string oscillates back and forth.
Finally, a book falling to the ground does not represent harmonic motion. Once the book is released from rest, we intuitively know that it will fall to the ground and will then stay there; in no way is there any periodic motion.
Example Question #2 : Harmonic Motion
If the mass of a simple pendulum is quadrupled, then its period __________.
doubles
is reduce to one quarter
remains the same
quadruples
remains the same
We know that the equation for the period of a simple pendulum is 
Example Question #4 : Harmonic Motion
A violin string 
Since we are solving for string tension, we need to use the frequency equation with the tension variable in it. That equation is 
We are given:
Next we must convert the length of 
Example Question #5 : Harmonic Motion
For a simple harmonic motion governed by Hooke's Law, 
We know that T is the period. The equation for T is 
Solve for 
Example Question #6 : Harmonic Motion
A pendulum on earth has a period of 
First, we need to find the length of the pendulum. Begin with the equation for finding the period of a pendulum:
solve for 
Now we can plug in our given values:
Since we have the length of the pendulum determined, we can now find the period of the pendulum on Mars:
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