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lec11-203-11-SHMmod3 - spring SHM F-kx k a x 0 m a 2 x 0 x...

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-kx F 0 x m k a m k ω 2 π ω = 2 π f = T T 1 f δ) ωt ( sin A x δ) ωt ( cos ω A v 2 a = -A ω sin ( ωt +δ) 0 x ω a 2 A=x max max v = A ω 2 max a = A ω spring SHM 11-0 L g ω Pendulum
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Examples: Spring, Pendulum… Most mechanical systems- displace from equilibrium- 2 possibilities restoring force 1 st approx F=-kx oscillates about equilibrium with natural frequency repulsive force - runs away Small displacement Simple Harmonic Motion Dynamics potential energy 1 st approx U=1/2 kx 2 3 Points to note hit (tickle) system it “rings” at a natural frequency (f o ) vibrate system with frequency (f)- it responds with f but close to (or at) f o get sharp, big “resonant” response friction makes natural ring die of exponentially with time 11-1
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