Problem Set 3

Physics 5200

Due 16 Feb. 1999

  1. (3 points) A 1mg mass oscillates with a frequency w 0 = 10kHz. A small amount of additional mass suddenly adheres to the original mass, lowering the frequency by 1Hz. How much additional mass was added? (This is a very sensitive way to measure small changes in mass.)
  2. (2 points) A piston executes simple harmonic motion with an amplitude of 0.1m. If it passes through the center of its motion with a speed of 0.5m/s, what is the period of oscillation?
  3. (3 points) A particle undergoes simple harmonic motion with a frequency of 10 Hz. Find the displacement x at any time t for the following initial conditions: at t = 0     x = 0.25m     [xdot] = 0.1m/s
  4. (2 point) What's the frequency of small oscillations for a mass m in a potential V(x) = -exp(-x2/2a2).