# Simple Harmonic Motion

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## Simple Harmonic Motion Answer Key

1.

A mass is connected to an ideal spring, as shown. As the amplitude [math]X[/math] increases, the period of the simple harmonic motion

- increases.
- decreases.
- some times increases and some time decreases, depending on the friction between the mass and the table.
- stays the same.

2.

A mass attached to an ideal spring is free to glide on a frictionless surface, as shown. At the point [math]x=0[/math],the kinetic energy of the mass reaches its

- minimum.
- maximum.
- average value.
- either maximum or minimum, depending on other factors.

3.

A block of mass [math]m[/math] is attached to an ideal spring is free to glide on a frictionless table, as shown. At the point [math]x=X[/math], the block's potential energy reaches its

- minimum.
- maximum.
- average value.
- either maximum or minimum, depending on other factors.

4.

In the system shown, the spring constant [math]k[/math] is quadrupled by parallely connecting three more identical springs. As a result, the period of the simple harmonic motion will .

- double
- quadruple
- decrease by a factor of 2
- decrease by a factor of 4

5.

In a simple pendulum, decreasing its length by a factor of 4 will .

- double its frequency
- quadruple its period
- decrease its frequency by a factor of 2
- decrease its period by a factor of 4

6.

Under what conditions does a pendulum exhibit a simple harmonic motion?

- Amplitude is small.
- Friction is negligible.
- Air drag is negligible.
- All of the above.

7.

Design an experiment to measure acceleration due to gravity [math]g[/math] using a simple pendulum.

- Measure the pendulum's period for several values of its length. Plot the line of best fit of length, in meters vs [math][/math][math]4pi^2T^2[/math], in [math]s^2[/math]. Acceleration due to gravity [math]g[/math], in [math]m/s^2[/math]is given by the line's slope.

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