Problems for
Intermediate Methods in Theoretical Physics

Edward F. Redish

Striking a Damped Cart

A small cart of mass m with (nearly) frictionless wheels is connected to a spring of spring constant k. It is connected to a plunger imbedded in light oil as shown in the figure at the right. The oil provides a damping force of -bv.

The cart is struck at time t = 0 by a quick tap with a hammer. We'll model this system by the equation of motion

(a) What are the dimensions of the constant A?

(b) Assuming that the cart is initially at x = 0 and is at rest, use the Fourier transform to solve for xt0(t),the position of the cart as a function of time when it is struck at a time t0.

(c) Show that for a general function, f(t), we can write


Show why this works, starting from the equation given above part (a). (You don't have to show that the solutions agree.)

This page prepared by

Edward F. Redish
Department of Physics
University of Maryland
College Park, MD 20742
Phone: (301) 405-6120

Last revision 12. December, 2005.