Simple Harmonic Motion -- Springs and Pendula

Simple Harmonic Motion

​Oscillating Springs and Simple Pendula

Open Ended

Way back at the start of the semester, we talked about uniform circular motion. UCM is an example of periodic motion. What does it mean if something is periodic?

Open Ended

One of the ways we can measure the periodic nature of circular motion is by finding its period. What is the period of an object in uniform circular motion?

Open Ended

One of the ways we can measure the periodic nature of circular motion is by finding its frequency. What is the frequency of an object in uniform circular motion?

Periodic motion:

• Motion that repeats itself over a regular interval over the same path.

• Period: The time it takes to complete one cycle/rotation/vibration (in seconds)

• Frequency: The number of cycles occuring every second (Hz)

​Video for Extra Support

This is a special type of periodic motion, where the motion is caused by a restoring force parallel to the path the object moves.

​

Simple Harmonic Motion (SHM)

• The spring force provided by Hooke's law is an example of a restoring force. Notice that the force is always parallel to the displacement.

Open Ended

Would uniform circular motion be considered a type of simple harmonic motion? Think about what direction centripetal forces act compared to the speed of an object.

TRY IT!

Find a bowl or basin that is shaped like a hemisphere on the inside. Place a marble inside the bowl and tilt the bowl periodically so the marble rolls from the bottom of the bowl to equally high points on the sides of the bowl. Get a feel for the force required to maintain this periodic motion. What is the restoring force and what role does the force you apply play in the simple harmonic motion (SHM) of the marble?

Here is another example of a vibrating spring going through simple harmonic motion. This time we have TWO restoring forces keeping the system in motion, depending on where the mass is relative to the rest position.

​

Oscillating Spring

Multiple Select

What force(s) could act as restorative to the vibrating spring on the previous slide? Remember, restoring forces should be parallel to the path of the motion. (Draw a free body diagram to help you if you're stuck!)

• Gravity

• Elastic Force

• Friction

• Tension

SHM and the Simple Pendulum

A Simple Pendulum follows the same principles:

A restoring force is provided that allows the pendulum to swing back and forth along the same path. Again, there is an easily measurable period and frequency of this motion.

Multiple Choice

What would the restorative force be for a pendulum undergoing simple harmonic motion?

• Tension

• Friction

• Elastic Force

• Gravity

SHM and the Simple Pendulum

GRAVITY is the restoring force!

Or at least one component is. The component of gravity that is tangent to the path of the pendulum is considered parallel to the motion.

​Video for Extra Support

All forms of simple harmonic motion have the properties of waves, including:

Waves and SHM

• Amplitude

• Frequency

• Period

​Maximum distance from rest position on either side.

Amplitude of Vibrating Spring

The maximum angle between the pendulum rod/string and the rest length.

NOTE: This is the other situation where our trig functions are reversed, just like with forces acting on an incline.

Amplitude of Simple Pendulum

Period of SHM

Let's think about how we can change the period of our vibrating spring system!

On go-el.com, you'll be able to log into our class collection of Gizmo simulations. You will conduct an experiment in the simulation to determine the factors affecting the period of a vibrating spring and a simple pendulum.

​

Simple Harmonic Motion Gizmo

Goals:

*Measure the period of a spring and a pendulum.

* Conduct controlled experiments to determine the effects of mass, the spring constant, and gravitational acceleration on the period of a spring.

* Conduct controlled experiments to determine the effects of mass, length, and gravitational acceleration on the period of a pendulum.

​Video for Extra Support