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Chapter 12 Vibrations and Waves Periodic Motion Any repeated motion Examples? Describe velocity, force and acceleration at a, b and c a c b c is the equilibrium or rest position The force is called the restoring force Any periodic motion where the restoring force is proportional to the displacement is called simple harmonic motion Frestore = -kDx Hooke’s Law Felastic = -kx spring force - because force is opposite displacement spring constant: how stiff the spring is x = displacement from rest position I have a mass of 85 kg. I jump on a trampoline and it compresses 40 cm before propelling me up. What is the spring constant of the trampoline? Felastic = Fweight Fweight = mg Fweight = 834 N x = 0.40 m k = -F/-x = 2085 N/m A pendulum moves in simple harmonic motion when displacement angles are small, less than 15° Forces on a Pendulum Net Force? acceleration? velocity? Net Force? acceleration? velocity? FT FT Fgy mg Fgx mg Time Measurements Period, T, is the time for one back and forth motion in seconds Frequency, f, is how often back and forth motions occur in 1 second, measured in hertz, Hz 1 f T 1 1 Hz sec Period of a Pendulum L T 2 g Period only depends on L, the length of the pendulum Period of a mass-spring system m T 2 k