F+T 4.6a Remember classical oscillators! For example,

Also,

b) This is basically an exercise in careful derivatives and moderately painful algebra. Take your time, double check each step as you go. It's an essential skill as a science major to be able to work your way through this kind of algebra without making any mistakes!

You know the answer (see Table 4-1 in F+T) so you can check your result at the end.

4-7 Requires very little real work, just some thinking.

4-8a,b) Think about double integrals from 2140, where we switched from rectangular to polar.

You may assume

the question is to find the proportionality constants.

4-9 Problem 1 (4.6 above) will help. Also, if MMA is going to do an integral for you numerically, you should change integration variables to dimensionless quantities.

4-10a) The amplitude of vibration tells you about the total energy, and if you know the frequency, you know something about the spring constant. (See hints for 4.6a!)

d) State your reasons.