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Chapter 13: S.H.M

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.

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Chapter 13: S.H.M

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  1. Chapter 13: S.H.M

  2. Simple harmonic motion is the projection of uniform circular motion on a diameter.

  3. dx dt d2x dt2 dv dt x = A Cos(t + ) v = = -  A Sin(t + ) 2  = = 2 f T a = = = - 2 A Cos(t + )

  4. mg mg L L F = -mg Sin  -mg  x = L  F  - x F = -kx k =  = max Cos(t + ) g k  = = m L

  5. d2x dx m + b + kx = 0 dt2 dt b  = 2m k b2 `= - m 4m2 k b2 ` 1 - f = = m 4m2 2 2 t Fdamping = -bv ma = -kx - bv Guess the Solution x = Ae-t Cos(`t) A : Underdamped B : Critical Damping C : Overdamping b2 << 4mk b2 = 4mk b2 > 4mk

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