Problem Set 3 (paper) due Wednesday 31 Mar 05

1. A mass of m = 6.00 kg is attached to a spring of spring constant k = 3000 N/m. The mass can slide along a frictionless, horizontal surface. The mass is pulled to stretch the spring by an amount x = 3.00 cm and the mass if thrown to the right with at v0 = 60.0 cm/s.
(a) Find the angular frequency of the SHM.
(b) Find the period of the SHM.
(c) Find the amplitude of the SHM.
(d) Find the frequency of the SHM.
(e) Find the phase constant (= initial phase) of the SHM.
(f) Find the total mechanical energy of the system.
(g) Find the speed of the mass when it passes through equilibrium.

2. A solid wooden log is floating in water. It has a height H, a cross sectional area of A and a density rhos. If I push the log down an additional distance x, the net force on the log is B = rhow gAx where rhow is the water density. Show that the motion of the log is SHM and find the period in terms of the variables mentioned above and any constants like g.

3. A physical pendulum is made from a rod of mass M and length L with a solid ball of mass (2M) and radius R=L/3. The center of the ball is located at the end of the rod as shown. The axis of rotation is at the left end. Find the period of the oscillation for small angle oscillations. The answer can only contain symbols M, L, and constants (numbers and g).

4. Here is the top view of a horizontal frictionless table witha mass, M, and two identical spring of relaxed length L0 and spring constant k. The mass is pulled away from the equilibrium a small amount x<< L0, stretching the springs by equal amounts, and it is released. Show that the resulting motion is not SHM.

This page maintained by Anne G. Young. Last modified 25-Mar-2005 .