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.

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Chapter 14

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Chapter 14

Chapter 14

Periodic Motion


Hooke s law

Hooke’s Law


Potential energy in a spring

Potential Energy in a Spring

See also section 7.3


Simple harmonic oscillator

Simple Harmonic Oscillator


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


In general

In general


Rewriting formulae

Rewriting Formulae

Equations


All equations looks the same

All equations looks the same

You want to write ALL oscillation equations in this form.


Solution

Solution


Natural frequency period etc

(Natural) Frequency, Period, etc…


Example

Example


What it looks like

What it looks like


X v a

x,v & a


Using initial conditions

Using initial conditions


Example1

Example

Given moment of inertia I and CM at l,

find the angular frequency.


Example2

Example


Simple pendulum

Simple Pendulum


Simple pendulum1

Simple Pendulum


Example3

Example

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


Energy of sho

Energy of SHO


Conservation of energy

Conservation of Energy


Energy of a pendulum reminder

Energy of a pendulum (reminder)


Energy of a pendulum

Energy of a pendulum


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Damped

Oscillation


Damping force

Damping Force

Fr


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Newton Second Law


Oscillations with damping

Oscillations with damping


Solving the equation

Solving the Equation

Try the solution:


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skip


Chapter 14 5658621

Skip


Three cases

Three Cases

Under-damped

Over-damped

Critically damped


Under damped

Under-damped


Under damped movie

Under-damped Movie


Chapter 14 5658621

  • Three cases:


Three cases1

Three Cases

Under-damped:

Over-damped:

Critically damped:


Chapter 14 5658621

Under-damped

Over-damped

Critically damped


Chapter 14 5658621

Under-damped

Critically damped

Over-damped


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under damped

over damped

critically damped

system slows down

fastest when

critically damped

Too much damping

Is counter-productive!


Resonance

Resonance

Pushing a swing


Driven forced oscillations

Driven / Forced Oscillations


Driven forced oscillations1

Amplitude A(ωd)

Driven / Forced Oscillations


Resonance1

Resonance


Resonance2

Resonance


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