University of Michigan Physics 340, Fall 2003 5 Sept. 2003 Assignment 1: The Harmonic Oscillator, Complex Representations, Superposition Required reading: French, Chap. 1 Chap. 2 through p 26 Chap. 3 through p 62 We start with a version of the basic physics problem for the harmonic oscillator: 1.A block of mass m=0.5 kg is free to oscillate at the end of a spring. At time t = 0, the block is launched from its rest position at x = 0, by a hammer strike which imposes an instantaneous velocity v0 = 40 cm/s. The block then executes simple harmonic motion with a maximum excursion of A = 10 cm. a)Find the oscillation frequency, the period, and the spring constant. (Hint: Write an expression for the position of the block as a function of time. Differentiate to find the velocity. Solve for the initial conditions.) b)What is the velocity at t = π/4 s? Explain. c)Plot the kinetic and potential energy of the block vs. time. (Recall that the potential energy of a linear spring is given by 212Ukx=.) What is the total energy vs. time?
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