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# Chapter 14 - PowerPoint PPT Presentation

Chapter 14. Periodic Motion. Hooke’s Law. Potential Energy in a Spring. See also section 7.3. Simple Harmonic Oscillator. Notations. This is the simple harmonic oscillation equation. Very very important!. You want to write ALL oscillation equations in this form. Simple pendulum.

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Chapter 14

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## Chapter 14

Periodic Motion

### Notations

This is the simple harmonic oscillation equation.

Very very important!

You want to write ALL oscillation equations in this form.

Simple

pendulum

Tuning

fork

Skyscraper

(Inverted Pendulum)

Equations

### All equations looks the same

You want to write ALL oscillation equations in this form.

### Example

Given moment of inertia I and CM at l,

find the angular frequency.

### Example

A lead ball is attached to a string 3m long. Find the natural period of the pendulum.

Damped

Oscillation

### Damping Force

Fr

Newton Second Law

### Solving the Equation

Try the solution:

### Three Cases

Under-damped

Over-damped

Critically damped

• Three cases:

### Three Cases

Under-damped:

Over-damped:

Critically damped:

Under-damped

Over-damped

Critically damped

Under-damped

Critically damped

Over-damped

under damped

over damped

critically damped

system slows down

fastest when

critically damped

Too much damping

Is counter-productive!

Pushing a swing

Amplitude A(ωd)