Lecture 2 Notes

Lecture 2 Notes - Recap of last lecture Chapter 13,...

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Recap of last lecture A restoring force which is directly proportional to the displacement from equilibrium will cause a periodic motion called SHM. Example a spring driven glider: Restoring force = F x = -kx or a x = d 2 x/dt 2 = -(k/m)x Chapter 13, Periodic motion

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Describing SHM Projection of an uniform circular motion on a plane.
Displacement, velocity and acceleration in SHM x = Acos θ θ = ϖ t+ φ x=Acos( ϖ t+ φ ) v x =dx/dt =- ϖ Asin( ϖ t+ φ ) a x =dv x /dt =- ϖ 2 Acos( ϖ t+ φ ) =- ϖ 2 x

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Displacement, velocity and acceleration in SHM Watch the simulation
Mathematical Description of SHM Projection of an uniform circular motion on a plane. x = A cos θ a Q = ϖ 2 R = ϖ 2 A a x = -a Q cos θ = - ϖ 2 Acos θ = - ϖ 2 x Using this notation on the spring we get ϖ 2 = (k/m) or ϖ = √(k/m) k m T m k 1 f = = For SHM frequency and period are independent of amplitude

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Problem 13.15 A 42.5 kg chair is attached to a spring and allowed to oscillate. When empty it takes 1.3 sec for one
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This note was uploaded on 01/27/2012 for the course PH 2233 taught by Professor Dipinkardutta during the Spring '11 term at Mississippi State.

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Lecture 2 Notes - Recap of last lecture Chapter 13,...

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