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# Student Exploration- Simple Harmonic Motion (answers)

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Author: Jack Bauer
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Student Exploration: Simple Harmonic Motion

Vocabulary: controlled experiment, harmonic motion, oscillation, pendulum, period, spring, spring constant

Prior Knowledge Questions (Do these BEFORE using the Gizmo.)

A bungee jumper launches herself off a bridge. How would you describe her motion?

A child goes to the playground and gets on a swing. How would you describe his motion?

What do the motions of the bungee jumper and swinger have in common?

Gizmo Warm-up

Harmonic motion is repeating back-and-forth or up-and-down movement. The Simple Harmonic Motion Gizmo™ allows you compare the harmonic motions of a spring and a pendulum.

To begin, open the TOOLS tab on the bottom right and drag one arrow to the bottom of the spring so that the weight just touches the tip of the arrow, as shown. Drag a second arrow so that the pendulum just touches the tip of the arrow when it swings to the left.

When the spring touches the arrow, click the green button on the stopwatch. Count the movements, or oscillations. Click the green button again after the tenth oscillation.

What is the time for 10 oscillations of the spring? _____________

Divide this time by 10 to find the period of the spring: _______________

Click the red button to reset the stopwatch. Use the same procedure on the pendulum.

What is the period of the pendulum? ____________________

Activity A:

Period of a spring

Get the Gizmo ready:

Click the red button to reset the stopwatch.

Introduction: The spring constant is a measure of the stiffness of a spring. The greater the spring constant, the harder it is to stretch or compress the spring. The Simple Harmonic Motion Gizmo allows you to manipulate the mass on the end of the spring (m), the spring constant (k), and the gravitational acceleration (g).

Question: Which factors affect the period of a spring?

Predict: Which factors do you think will increase or decrease the period of a spring? Which do you think will have no effect on the period of a spring?

Gather data: In a controlled experiment, only one factor changes at a time. Controlled experiments are a fair way to compare the effects of each variable on a system.

For each of the combinations given in the table below, measure the time for 10 oscillations of the spring and calculate the period. If necessary, reduce the Sim. speed to improve your accuracy.

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