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Oscillatory_Motion_0212_handout

Oscillatory_Motion_0212_handout - Oscillatory Motion This...

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cceleration in One Dimension PHYS 0212 Oscillatory Motion 1 Oscillatory Motion This experiment has four parts: 3. Determine spring constant k for an inertial balance 2. Determine g using a simple pendulum (2 different bobs) 4. Study the pendulum motion of your arms and legs as you walk Photogate Works like a TV or DVD remote control. The computer records the times when the gate is blocked and unblocked. Picket Fence Used to measure acceleration with one photogate. 1. Determine g using a photogate and picket fence x x x x x x x x PHYS 0212 Oscillatory Motion 2 Photogate Acceleration of a Free Falling Body ( ) 1 1 1 2 n n n n n v v a T T + + = + , , PHYS 0212 Oscillatory Motion 3 The Simple Pendulum L L mg x bob θ We can determine the motion of the simple pendulum by looking at the torque acting on the center of mass. Fx τ = F mg = − sin x L θ = ( )( ) sin sin mg L mgL τ θ θ = − = − The lever arm: sin mgL τ θ = − PHYS 0212 Oscillatory Motion 4 Displacement cos A t L L ω θ = = The Small Angle Approximation If an angle is measured in radians and it is very small then we can use the small angle approximation: You can try this on your calculator. Set the mode to “radians” (rad) and take the sine of 0.1. The answer should be 0.0998, which is very close to 0.1. sin θ θ Difference 1% for 14 θ ° sin mgL mgL τ θ θ = − = − Now we can write the torque as: Note that for Simple Harmonic Motion: cos A mgL mgL t L τ θ ω = − = − ( ) cos mg A t τ ω = −
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cceleration in One Dimension PHYS 0212 Oscillatory Motion 5 I τ α = 2 cos a A t L L ω ω α = = 2 2 cos cos A t I I A t L L ω ω ω τ ω = = ( ) 2 cos I A t L ω τ ω = −
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