MCAT Physical : Other Harmonic Motion Principles
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Example Question #1 : Other Harmonic Motion Principles
A long pendulum with a length of 
We are asked for the period of the pendulum, or the time it takes to make one full revolution or swing.
The period of a pendulum is given by this formula:
Where 
It takes roughly 12 seconds for the pendulum to make a full swing. Note that the mass attached to the end of the pendulum is irrelevant.
Example Question #1 : Other Harmonic Motion Principles
A spring is compressed as far possible and is not permitted to expand. What can be said about its potential energy and its kinetic energy?
Its potential and kinetic energy are both at a maximum
Its potential energy is at a maximum and its kinetic energy is at a minimum
The total energy of the spring is zero
Its potential energy is at a minimum and its kinetic energy is at a maximum
Its potential energy and kinetic energy are both at a minimum
Its potential energy is at a maximum and its kinetic energy is at a minimum
In this case, the kinetic energy of the spring is at a minimum. This is because, as the question indicates, the spring is not moving. At the same time, because the spring is compressed as far is it can be compressed, we know that its potential energy is at a maximum. The total energy of the spring therefore cannot be zero.
Example Question #2 : Other Harmonic Motion Principles
Which of the following changes to a pendulum would decrease its period?
Increasing the mass of the weight at the end of the pendulum
Starting the pendulum from a greater height
Decreasing the density of the pendulum
Increasing the length of the pendulum
Decreasing the gravitational attraction involved
Increasing the length of the pendulum
The only factor that affects the period of a pendulum is the length of the pendulum. Therefore we can ignore any of the other answers which include other factors. The equation for the period of a pendulum is:
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