Oscillations and Waves

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Oscillations and Waves

• Energy Changes During Simple Harmonic Motion

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Energy in SHM Energy-time graphs
Note For a spring-mass system KE ½ mv2 ?
KE is zero when v 0 PE ½ kx2 ? PE is zero
when x 0 (i.e. at vmax)
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Energydisplacement graphs
Note For a spring-mass system KE ½ mv2 ?
KE is zero when v 0 (i.e. at xo) PE ½ kx2 ?
PE is zero when x 0
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Kinetic energy in SHM We know that the velocity
at any time is given by v ? v (xo2 x2) So
if Ek ½ mv2 then kinetic energy at an instant
is given by Ek ½ m?2 (xo2 x2)
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Potential energy in SHM If a - ?2x then the
average force applied trying to pull the object
back to the equilibrium position as it moves away
from the equilibrium position is F - ½ m?2x
Work done by this force must equal the PE it
gains (e.g in the springs being stretched).
Thus.. Ep ½ m?2x2
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Total Energy in SHM Clearly if we add the
formulae for KE and PE in SHM we arrive at a
formula for total energy in SHM ET ½
m?2xo2 Summary Ek ½ m?2 (xo2 x2) Ep
½ m?2x2 ET ½ m?2xo2
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