{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

PS1_03 - University of Michigan Physics 340 Fall 2003 5...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
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 v 0 = 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 2 1 2 U kx = .) What is the total energy vs. time?
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Ask a homework question - tutors are online