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11.1 Simple Harmonic Motion Periodic oscillations

Restoring Force: F = -kx

Force and acceleration are not constant

Amplitude (A) is maximum displacement

Frequency is Tf 1

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11.1 Simple Harmonic Motion The system is in equilibrium is when ΣF

= mg - kxo

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11.2 Energy in the Simple Harmonic Oscillator Combination of KE and PE

When v = 0 then

Since energy is conserved then

22

21

21 kxmvE

2

21 kAE

)( 22 xAmkv

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11.3 Sinusoidal Nature of Simple Harmonic Motion

Compare uniform circular motionto the motion on a spring.

TAv 2

max

kmT 2

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11.3 Sinusoidal Nature of Simple Harmonic Motion

)T

t π2cos(A) tωcos(Ax

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11.3 Sinusoidal Nature of Simple Harmonic Motion

mkAv max

mkAa max

Ax max

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11.4 The Simple Pendulum The restoring force

is due to gravity

If the angles are small then

sinmgF

xLmgF

gLT 2

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11.5 Damped Harmonic Motion

Tuned Mass Damper Seismic Spring Dampers

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In class: Problems 3, 14 Other problems ↓

4. (a)

(b) The amplitude is the distance pulled down from equilibrium

The frequency of oscillation is found from the total mass and

the spring constant.

A = 0.025 m