Lesson 32 OSCILLATORY MOTION AND SIMPLE HARMONIC MOTION
 Name: etp       Section: M1       Start Time: 14:1:30       Instructor: Dr Evelyn E_Patterson       Course: 110H

1) An oscillation is a physical phenomenon characterized by the fact that the configuration of a physical system repeats (or almost repeats) itself over and over again. Simple harmonic oscillations are a special case of this. An oscillation is simple harmonic if the period (the time for one cycle) does not depend on the amplitude (the maximum displacement from equilibrium.)

In the following set, identify the oscillations that are simple harmonic, the ones that are approximately simple harmonic, and the ones that are not simple harmonic. Feel free to comment on why/how you make your identifications.

1. The pendulum in a grandfather clock
2. A boat in water pushed down and released
3. A child on a swing
4. A mass hanging from a spring
5. A ping pong ball bouncing on the floor.

2) A 0.100 kg mass is oscillating on a vertical spring of spring constant 200 N/m. The mass moves up and down a total of about .16 m as it oscillates. For this system, estimate the

1. amplitude
2. frequency
3. angular frequency, and
4. period.

What could you do if you wanted the period to be twice as long?

Suppose the mass stops oscillating and is just hanging, at rest, from the spring. Does the mass-spring system have any gravitational potential energy then? Does it have any spring potential energy then? (We'll discuss these points in class!)

3) One way to characterize simple harmonic motion is to say it is the motion that results when an object is subjected to a restoring force that is proportional to the object's displacement from its equilibrium position. For an object whose mass is constant, we know that Newton's second law says the force Fnet = ma = m d2x/dt2. Thus, for simple harmonic motion, if x represents the displacement from equilibrium, we can say:

Suppose we have a situation for which
.

Could the motion described by this equation be simple harmonic motion, or approximately simple harmonic? What would you need to do with the f(x) in order to determine the conditions for which the motion might be simple harmonic?

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