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11/18 Simple Harmonic Motion HW “Simple Harmonic Motion” Due Thursday 11/21 Exam 4 Thursday 12/5 Simple Harmonic Motion Angular Acceleration and Torque Angular Momentum I’m out of town Monday 12/2 (after Thanksgiving) Simple Harmonic Motion (SHM) Real objects are “elastic” (to some extent) Elastic: Object returns to original shape after deformation Original shape called “Equilibrium” Object resists deformation with force Force called “Restoring Force” Force proportional to deformation Force is in opposite direction to deformation Force points toward equilibrium, deformation points away from equilibrium Simple Harmonic Motion (SHM) Definitions: Displacement x “deformation from equilibrium” Equilibrium Fnet = 0 as usual Oscillation one complete cycle Period T time for one complete oscillation Frequency f # of oscillations in one second example: 1.65Hz (in units of “Hertz”) Amplitude A maximum displacement from equilibrium Hooke’s Law = Simple Harmonic Motion Force always points toward the equilibrium position. FSpring = -k x x is displacement (compression or extension) from equilibrium. “Simple” harmonic motion only when the force is proportional to the displacement, x, as in Hooke’s law. Equilibrium Position, Fnet = 0 m k greatest displacement right (x = A) FS,B points left = Fnet = -kx complete oscillation, # of seconds = T (Period) greatest displacement left (x = A) FS,B points right = Fnet = -kx motion is symmetric, max displacement left = max displacement right Warning!!!! The acceleration is not constant so a v/t !!! k m vave “mid-time” velocity!!! Fnet does equal ma, however greatest displacement up (x = A) WE,B - FS,B points down = Fnet = -kx measure x from equilibrium position Equilibrium Position Fnet = 0 greatest displacement down (x = A) FS,B - WE,B points up = Fnet = -kx measure x from equilibrium position motion is symmetric, max displacement up = max displacement down A complete oscillation, # of seconds = T (Period) Fnet = -kx Fnet = ma What we find: m T 2 k 2 f 1/ T l g A block hangs from a spring and is pulled down 10 cm and released. It bounces up and down at a rate of 3 times every second. How could this rate be increased? You may choose any of: increase the mass decrease the mass push it faster make the spring stiffer make the spring less stiff pull it down farther don’t pull it down as far other? What matters? Period (or frequency) affected by: spring constant (k) Yes mass (m) Yes amplitude (A) No initial conditions No (how we get it going)