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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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Presentation Transcript
chapter 14

Chapter 14

Periodic Motion

potential energy in a spring
Potential Energy in a Spring

See also section 7.3

notations
Notations

This is the simple harmonic oscillation equation.

Very very important!

You want to write ALL oscillation equations in this form.

other examples
Simple

pendulum

Tuning

fork

Skyscraper

(Inverted Pendulum)

Other Examples
all equations looks the same
All equations looks the same

You want to write ALL oscillation equations in this form.

example1
Example

Given moment of inertia I and CM at l,

find the angular frequency.

example3
Example

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

slide25
Damped

Oscillation

solving the equation
Solving the Equation

Try the solution:

three cases
Three Cases

Under-damped

Over-damped

Critically damped

three cases1
Three Cases

Under-damped:

Over-damped:

Critically damped:

slide38
Under-damped

Over-damped

Critically damped

slide39
Under-damped

Critically damped

Over-damped

slide40
under damped

over damped

critically damped

system slows down

fastest when

critically damped

Too much damping

Is counter-productive!

resonance
Resonance

Pushing a swing

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