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October 30.doc

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McGill University
PHYS 101
Kenneth Ragan

Phys 101 Alanna Houston October 30, 2007 - Hooke’s Law: F = -kx - x = 0 is the equilibrium position - +ve x is towards extension - Force is always opposite displacement so it works to bring back object (always a restoring force) - Motion through one complete cycle, starting from a compressed and motionless state: - - When x is at equilibrium position, then speed is maximum and F is 0 - Motion is Periodic and oscillatory: simple harmonic motion (SHM) - In SHM or an SHO, F ~ -x - T is time for one complete motion related to frequency by T = 1/f - Since force is always changing, so is acceleration therefore you CANNOT use constant accelerations formula - Instead you have to use energy formulae. - - Last one for frictionless surface Phys 101 Alanna Houston - The total energy in a system is proportional to the square of the amplitude of the oscillation - At equilibrium: - In general, at any arbitrary point: - - Example: When a spring stretches 0.150m when a 0.300 kg mass is lowered GENTLY on it. Spring is then set up horizontally with the same mass on a frictionless table, and pulled 0.100 m from the equilibrium point. Find a)k, b)A, c)vmax, d)v when mass is 0.050 m from equilibrium, e)amax o A) mg = kx when x = 0.250 m. Therefore, k = 19.6 N/m. o B) A = 0.100 m o C) Vmax = Asqrt(k/m) = 0.1(sqrt(19.6/0.3)) = 0.81 m/s o D) v = Vmax(sqrt(1-x^2/A^2)) = 0.81*sqrt(1- (0.05/0.1)^2)= 0.7 m/s o E) amax = kx, when x is max…at two max points. Therefore, amax = kA/m. amax = 19.6*0.1*0.3 = 6.5 m/s^2 - To look at period of simple harmonic motion, use uniform circular motion viewed from the side - Phys 101
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