1. (4) Marion & Thornton: problem 3-18. Hint: To calculate the energy lost during one period, calculate the work done by the frictional force in one period. This means doing an integral! I suggest you change the integration variable from dx to (xdot dt).

2. (4) Marion & Thornton, problem 3-20. Do this problem by hand (algebra), not using the computer.

3. (4) Marion & Thornton, problem 3-24. Rather than put three plots on a single graph, I suggest that you plot x_p(t) and x_c(t) together, but then plot their sum x(t) separately. (Otherwise it will be too hard to read.) To put two plots on the same graph using Mathematica, put the two functions inside curly brackets separated by a comma, like this:

Plot[{x^2, Sin[x]},{x,0,4}]

4. (5) Marion & Thornton, problem 3-28. Do this problem from scratch. Start by deriving the differential equation for the charge on the capacitor using Kirchhoff’s laws, with the driving voltage of the form V(t) = V₀cos(w t). Now try a solution of the form q = q₀cos(w t-d), and calculate both q₀ and d . After you have done all this, you will see that the amplitude of the current qdot(t) is proportional to the driving frequency w when w RC << 1. (The product RC is called the time constant of the circuit.)

5. (4) Marion & Thornton, problem 3-29.

6. (4) Marion & Thornton, problem 3-32. You may use Mathematica to make the plots.