Medradsc 1c03

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Medradsc 1c03
Dr Fiona McNeill Waves and Vibrations
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Simple Harmonic Motion
x
Fapplied
Frestoring
Frestoring -kx
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Simple Harmonic Motion
x
Fapplied
Frestoring
Frestoring kx
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(No Transcript)
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Simple Harmonic Motion
xA
x-A
In a frictionless system, m will oscillate
indefinitely between the positions xA and
x-A The position x is a sinusoidal function of
time, t, XA sin(?t)
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Simple Harmonic Motion
xA
x-A
XA sin(?t) ? is called the angular frequency of
the oscillation Its SI unit is radians per second
(rad/s) 2p radians 360 , p radians 180
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Simple Harmonic Motion
xA
x-A
XA sin(?t) Where ?v(k/m)
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Period
? is related to the period, T This is the time
taken to go from A to A and back to A ??t 2p
for this time so ? 2p /T or T 2p / ?
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Frequency
The frequency is the number of complete
oscillations per second f 1/T and since T 2p
/ ? f ? / 2p
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Phase Angle
xA sin(?t) xA sin(?td)
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Damped Harmonic Motion