The Physics Philes, lesson 76: Oscillation Vacation
Hello, my fellow physics fanatics! Because of Thanksgiving break I nearly forgot about this post. But never fear! I shall not abandon you!
It is a bit of sad week, however, as last week was the final lesson on gravity. (You may have noticed that we did not cover the coolest and most mysterious gravitational topic of them all – black holes. However, we covered them extensively here and here, so I thought it would be OK to skip them.)
So it’s sad, but it’s also happy because we get to start in on a whole new topic! It’s time to begin our journey into periodic motion.
Periodic motion, also called oscillation, is basically motion that repeats itself. Like a pendulum or sound vibrations. We need to understand oscillation in order to understand waves, sound, electric currents, and light. So, yeah. It’s pretty important stuff.
To understand oscillation, let’s think about a body sitting on a frictionless surface (like an air track) so it can move along the x-axis. Now think of that same body attached by a spring of negligible mass to one end that can be compressed or stretched. The spring is fixed on the left side. Like this:
The vertical normal and gravitational forces add up to zero and the force of the spring is the only horizontal force acting on the body.
Every body that oscillates always has a stable equilibrium position. When it’s moved away from that position and then released, a force or torque will act and bring it back to that stable position. However, in moving back to equilibrium, the body will pick up some kinetic energy and overshoot. When the body stops on the other side, a force or torque will pull it back to equilibrium. It then overshoots, and the whole thing starts all over again.
In our little diagram above, let’s say that the body is sitting at equilibrium and we can consider that spot the origin. As the spring is compressed or stretched, we can consider it to be moving along the x-axis. The distance the body is moved from its equilibrium origin is called the displacement. Whenever a body is displaced, a force tends to try to restore the body to its equilibrium position. This force is called the restoring force. Oscillation can only occur if there is a restoring force.
There are few other things we need to define before we move on. The amplitude of the motion is the maximum magnitude of the displacement, and it’s always positive. Think about the height of a wave. It’s like that.
A cycle is a complete vibration. It’s one round trip. Think of pendulum. It swings forward, then back past the origin, then back to the origin. The period is the time of one cycle. The frequency of the oscillation is the number of cycles completed in a unit of time. The SI unit for frequency is herzt, and one hertz is equal to one cycle per second.
Finally we have angular velocity. It’s 2Π times the frequency. This represents the rate of change of the angular quantity and is always measured in radians.
OK! We have the tools we need to learn about oscillation. I’ll give you some time to mull this over and I’ll be back next week to discuss simple harmonic motion.
Featured image credit: Christopher Carfi via Flickr