W11Physics1CLec12C

# W11Physics1CLec12C - Physics 1C Lecture 12C Note Problem...

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Physics 1C Lecture 12C Note: Problem Session Wednesdays 8-9:50pm Peter 110

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Simple Pendulum The simple pendulum is another example of simple harmonic motion. Making a quick force diagram of the situation, we Fnd: The tension in the string cancels out with a component of the gravitational force ( mg cos θ ). This leaves only the perpendicular component causing acceleration.
Simple Pendulum Looking back at Hooke’s Law: In this case we have: F g , x = ! mg sin " ! F ! = ! F restoring = " constant ( ) displacement ( ) It doesn’t seem to follow the pattern for Hooke’s Law. But at small angles ( θ <30 o ), we can say that θ sin θ ( if θ is in radians )

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Simple Pendulum In the tangential direction: θ = max cos ( ω t + φ ) The length, L , of the pendulum is constant and for small values of : This confirms the form of the motion is SHM! General solution: tan ! = s L " d 2 s dt 2 = L d 2 dt 2 d 2 dt 2 = " g L
Simple Pendulum The angular frequency is: The period is: The period and frequency depend only on the length of the string and the acceleration due to gravity The period is independent of the mass

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Pendulum Period All simple pendula that are of equal length and are at the same location (same g ) oscillate with the same period Please note that the period of a pendulum depends on different variables than the period of a mass on a spring
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W11Physics1CLec12C - Physics 1C Lecture 12C Note Problem...

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