Oscillatory_Motion_0212_handout

Oscillatory_Motion_0212_handout - Oscillatory Motion This...

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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 nn n vv a TT + + = + 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 xL = ( ) sin sin mg L mgL θθ The lever arm: sin mgL PHYS 0212 Oscillatory Motion 4 Displacement cos A t L L ω == 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 Difference 1% for 14 ≤° sin mgL mgL Now we can write the torque as: Note that for Simple Harmonic Motion: cos A mgL mgL t L θω    cos mg A t
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PHYS 0212 Oscillatory Motion 5 I τ α = 2 cos aA t L L ω == 22 cos cos At I I LL ωω  −−   () 2 cos I A t L =− We also know that torque is equal to: Where I is the moment of inertia and is the angular acceleration.
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This note was uploaded on 08/17/2008 for the course PHYS 0212 taught by Professor Naples during the Spring '08 term at Pittsburgh.

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Oscillatory_Motion_0212_handout - Oscillatory Motion This...

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