# 6bsgmidterm1 - Study Guide for Midterm 1 Simple Harmonic...

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Study Guide for Midterm 1 Simple Harmonic Motion (undamped) An object of mass m is connected to a spring with spring constant k . x = 0 is the position of equilibrium. At t = 0 s, the object has initial position x (0) and initial velocity v (0). The equation of simple harmonic motion is d 2 x dt 2 + ω 2 x = 0 Other important quantities and equations are x ( t ) = A cos( ωt + φ ) v ( t ) = dx dt = - ωA sin( ωt + φ ) a ( t ) = dv dt = - ω 2 A cos( ωt + φ ) ω = r k m = 2 πf period : T = 1 f = 2 π ω potential energy : U ( t ) = 1 2 kx ( t ) 2 kinetic energy : K ( t ) = 1 2 mv ( t ) 2 U ( t ) + K ( t ) = E total = 1 2 kA 2 = constant a ( t ) = - ω 2 x ( t ) x ( t ) 2 + v ( t ) 2 ω 2 = A 2 amplitude : A = r x (0) 2 + v (0) 2 ω 2 A cos φ = x (0) A sin φ = - v (0) ω φ = arctan - v (0) ωx (0) , see below ! Here is an important message regarding the last equation above. If you take the arctan of a NEGATIVE number, the calculator will give you an answer (call it θ ) that’s either 1

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• Fall '08
• Williams

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