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Chapter 13: S.H.M. Simple harmonic motion is the projection of uniform circular motion on a diameter.. dx. dt. d 2 x. dt 2. dv. dt. x = A Cos(t + ). v = = - A Sin(t + ). 2. = = 2 f. T. a = = = - 2 A Cos(t + ). mg. mg. L. L. - PowerPoint PPT Presentation
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Fdamping = -bv
ma = -kx - bv
kx = 0d2xdt2
m dxdt
b+ +
= b2m
`= km
b2
4m2-
km
b2
4m2-f = 1
2`2
=
Guess the Solution x = Ae-t Cos(`t)
A : Underdamped B : Critical DampingC : Overdamping
b2 << 4mk b2 = 4mkb2 > 4mk
t