### All MCAT Physical Resources

## Example Questions

### Example Question #21 : Rotational, Circular, And Harmonic Motion

A long pendulum with a length of has a mass attached to the end of it. Approximately how long does it take for the pendulum to swing one time from its maximum displacement?

**Possible Answers:**

**Correct answer:**

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 and

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 #2 : 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?

**Possible Answers:**

The total energy of the spring is zero

Its potential energy is at a maximum and its kinetic energy is at a minimum

Its potential energy and kinetic energy are both at a minimum

Its potential energy is at a minimum and its kinetic energy is at a maximum

Its potential and kinetic energy are both at a maximum

**Correct answer:**

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 #1 : Other Harmonic Motion Principles

Which of the following changes to a pendulum would decrease its period?

**Possible Answers:**

Decreasing the density of the pendulum

Increasing the mass of the weight at the end of the pendulum

Decreasing the gravitational attraction involved

Starting the pendulum from a greater height

Increasing the length of the pendulum

**Correct answer:**

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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