Chapter 14
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Chapter 14 PowerPoint PPT Presentation


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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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Chapter 14

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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

Tuning

fork

Skyscraper

(Inverted Pendulum)

Other Examples


In general


Rewriting Formulae

Equations


All equations looks the same

You want to write ALL oscillation equations in this form.


Solution


(Natural) Frequency, Period, etc…


Example


What it looks like


x,v & a


Using initial conditions


Example

Given moment of inertia I and CM at l,

find the angular frequency.


Example


Simple Pendulum


Simple Pendulum


Example

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


Energy of SHO


Conservation of Energy


Energy of a pendulum (reminder)


Energy of a pendulum


Damped

Oscillation


Damping Force

Fr


Newton Second Law


Oscillations with damping


Solving the Equation

Try the solution:


skip


Skip


Three Cases

Under-damped

Over-damped

Critically damped


Under-damped


Under-damped Movie


  • 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!


Resonance

Pushing a swing


Driven / Forced Oscillations


Amplitude A(ωd)

Driven / Forced Oscillations


Resonance


Resonance


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