444444444 - PY211 Lecture 22(22 Nov 2016 Periodic Motion[Ch...

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PY211 Lecture 22 (22 Nov 2016) Periodic Motion [Ch. 14 Young and Freedman (cont.)] Temperature and Heat [Ch. 17 Young and Freedman]
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Class info Final exam: on Friday, Dec. 16, 6:00-8:00pm – in CGS-129 – Cumulative, but including all of the new material Problem Set 9: due next Friday, Dec. 2 by 5pm. – Ten problems online. Half also submitted on paper • Discussion next week: on topics from Chs. 17, 18. Help: SCI-121 More help: on Piazza.com!
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SHM: Mass on a spring • The general equation of motion for SHM is: where For the specific case of a mass m on a spring with spring constant k , we can derive an eq. of motion: from or • So
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Other applications of SHM For other systems, we analyze the equation of motion and see if it looks like simple harmonic motion. τ = I α = κθ d 2 θ dt 2 + κ I θ = 0 F = ma = kx d 2 x dt 2 + k m x = 0
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Quick Quiz For very small angles, 1. 2. 3. 4. 5. sin θ 0 θ θ θ 3 3! θ θ 3 3! + θ 5 5! 1 ( ) n 2 n + 1 ( ) ! θ 2 n + 1 n = 0 How small is small for sin θ θ ?
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SHM: Simple pendulum For a simple pendulum consisting of a mass m on a string of length l , start with the sum of the torques: • So For small angles , the equation of motion is: and
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Worksheet A simple pendulum on a string of length 4.0 m swings from one side to the other (a total angle of 18 o ) in 2.0 s. – Write an expression for the angular displacement of the pendulum, if it passes through the bottom at time t = 0 with positive velocity, and graph θ vs. t.
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