Which of the following functions x t has a second derivative which is proportional to the negative of the function Lecture 26 Hooke s Law De ne system choose coordinate system Draw free body diagram Hooke s Law F kx Newton s Second Law kx m Concept Question Answer 4 x t Acos Simple Harmonic Motion SHM Equations Frequency Angular frequency Position Velocity Initial Position at t 0 Initial Velocity at t 0 General Solution General Solution Simple Harmonic Oscillator SHO Equations Equation of kx mx t Mass on a spring Energy x t Acos w t o v t w Asin w t o w A Constant energy oscillates between kinetic and potential energies K t U t E constant Worked Example Fluid Oscillations in a U tube A U tube open at both ends to atmospheric pressure is lled with an incompressible uid of density r The cross sectional area A of the tube is uniform and the total length of the column of uid is L A piston is used to depress the height of the liquid column on one side by a distance x and then is quickly removed What is the frequency of the ensuing simple harmonic motion Assume streamline ow and no drag at the walls of the U tube The gravitational constant is g U y mgy K
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