Physics 261: Problem Set #4

1. To start, ask for help with ?Series. Express the accuracy of the approximations with one, two, and three terms as a percent error (that is, calculate the difference between the approximate answer and the exact answer, divided by the exact answer). It's convenient to do these numerical calculations in Mathematica as well!
2. (K+K 2.28) This is easiest in cylindrical coordinates (r, theta, z). Remember that the car must accelerate radially to go in a circle. If the car is going around a circular arc, what is r double-dot?
3. (K+K 2.31) In part a), include a coordinate for the point joining the springs as well as one for the mass. What is the net force on the point? (This gives a relation between the coordinates.)
   To identify the frequency, you only need to write Newton's law in the form of Example 2.17. There is an analogy between the springs here and capacitors in series or parallel!
4. (K+K 2.33) Note that the only force on the sliding mass is in the theta-direction. What does that tell you about the radial acceleration? This is a differential equation for r(t), and your job is to verify that the function given in the book satisfies it.
5. (K+K 2.23) The dependence on Delta theta drops out in the end! Look at Newton's 2nd law in polar coordinates.