PHYSICS 321 - Classical Mechanics I

Spring 2007

Homework Set #5 (due 2/21/07)

1. Thornton and Marion, problem 3-1.

2. Thornton and Marion, problem 3-2.

3. Thornton and Marion, problem 3-3.

4. Thornton and Marion, problem 3-6.

5. Thornton and Marion, problem 3-13. Hint: calculate the time derivatives of the x(t) given in the problem, and plug them into the damped harmonic oscillator equation (3.35) with the condition that ω₀² = β². This will give you a simple differential equation for y(t).

6. Consider a mass m hanging vertically from the end of a spring of force constant k. In equilibrium, the mass rests at a position y = y₀ = mg/k. Starting from Newton’s second law, show that if the mass is displaced from equilibrium a distance A and then released, it will follow simple harmonic motion about the position y₀.