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# ps01 - Physics 214 Problem Set#1(Due by 11:15 am Thursday 1...

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1 Physics 214 Problem Set #1 (Due by 11:15 am, Thursday 9/4/08) 1. At the right is a plot of F ( x ) versus x , the force experienced by a particle in the x direction as a function of its position x . At which point or points may the particle undergo simple harmonic motion, when it is initially displaced by a small Δ x ? Explain briefly. 2. Two objects, 1 and 2, oscillate with the same frequency but with different amplitudes, phase constants, and equilibrium points. (a) Determine the values of all constants in the equations x 1 ( t ) = x eq1 + A 1 cos ( ω t + φ 01 ) and x 2 ( t ) = x eq2 + A 2 cos ( ω t + φ 02 ) from the graphs of x 1 ( t ) and x 2 ( t ) shown below. 0 1 2 3 4 5 6 1 0.5 0 0.5 1 1.5 2 t (sec) x1 (mm) x2 (mm) (b) Find the maximum velocity and maximum acceleration of object 1. (c) Show the total mechanical energy—the sum of kinetic and potential energies—is constant. (d) x 1 “leads” x 2 —that is, x 1 reaches its maximum (or zero crossing or minimum) before x 2 does by a time interval Δ t . What is the numerical value of Δ t ?

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