# Restoring Forces & Oscillation: Definition & Examples Video

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• 0:03 Pendulums and Springs
• 0:35 Spring Oscillators
• 2:21 Simple Pendulum
• 3:59 Lesson Summary
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Lesson Transcript
Instructor: Matthew Bergstresser
Restoring forces are what makes systems oscillate. In this lesson, we will investigate how restoring forces are involved in the motion of masses attached to springs and simple pendulums.

## Pendulums and Springs

Have you ever seen someone bungee jump? They jump off of a bridge over a river attached to a special elastic cord that causes them to oscillate up and down after they almost reach the river's surface. This is one type of oscillating system. The other type is when a cord has a mass tied to one end and it swings back and forth, which is called a pendulum. Think of a rope swing. Let's investigate these two types of oscillators.

## Spring Oscillators

Let's pretend we have a frictionless surface with a spring attached to an upright. Attached to the spring is a mass. This diagram shows the rest length of the spring. When the spring is at this length, there are no forces acting on it.

This diagram shows the compressed spring attached to the mass.

When the mass is let go, the spring applies a force that varies with the compressed length of the spring until it reaches its rest length. This causes the mass to accelerate up until it reaches the equilibrium position. This diagram shows the mass at the equilibrium position.

Even though there is no spring force acting on the mass at this location, it continues to move to the right due to its momentum. As soon as the spring begins to stretch past the equilibrium point, it applies a force in the opposite direction of the mass's motion. This diagram shows the mass after it has passed the equilibrium point.

The force is directed opposite the direction of motion of the mass. Eventually, the mass will come to a stop and then accelerate back towards the equilibrium position.

Again, the spring force varies with the distance the spring stretches past the equilibrium point. The spring force is a restoring force because it always applies a force towards the equilibrium point. When the mass reaches the equilibrium point on its way back to where it started, there will be no restoring force on the mass. The mass's momentum will take it past the equilibrium point. The spring force will then change directions and point to the right again. This will cause the mass to oscillate back and forth. Now let's look at another oscillator called a simple pendulum.

## Simple Pendulum

Have you ever swung out over a body of water on a rope swing? If so, you were part of a simple pendulum, which consists of a cord attached at a fixed point with a mass at the other end. The equilibrium point for a simple pendulum is when the mass is hanging straight underneath the point where the cord is attached at the fixed point. This diagram shows a simple pendulum at its equilibrium position.

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