PHYSICS 321  -  Classical Mechanics I

 

Spring 2010

 

Homework Set #5 (due 2/24/10)

 

 

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.