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Problems 4.8-4.13.

If a problem involves determining an approximate numerical solution, you must write your own program using Euler's method in a compiled language. Using ode45() in matlab or lsode() in octave is not allowed.

In problem 4.8, you only need to do the plots for the first three equations.

Are we to assume that F(t)=mg or mg is an additional force to F(t)?

The latter. Assume there is some unspecified applied force F(t) as well as gravity.

Someone asked me:

1. In problem 4.8, I keep getting numerical method solutions and approximations that are mirror images of one another over the x-axis. Having talked to several others who get the same thing, is this the way it's supposed to be?

2. In problem 4.9, do you want only the equation of motion or must we also solve it for x as a function of t?

For number 1 all I can think of is that perhaps it's due to the phase angle. Are you including \phi when you do the plot? If \phi is close to 180 degrees, then they will be out of phase. Other than that, I can't think of a reason why this is happening. The answers should be about the same in steady state (maybe not initially).

For 2, the question asks just for the equations of motion, not the solution. You should see that when gravity is included, as long as x is measured from the equilibrium position, the equation of motion is the same.