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Unformatted text preview: mine if the total energy behaves the way that you expect. Notice that the way in which we have given the initial conditions, that the magnitude of the total energy depends on dt . As you increase dt , at some point you should produce poor results. Make an argument for how small the time step needs to be for good integration (Hint: what is the relevant time scale set by the problem?). 5. Add a damping and driving force to the problem, so that the equation of motion you will solve for is, m d 2 y dt 2 + v + ky = F cos t. (2) where the velocity v = dy dt Write a new code using the one in the handout that you were given as a starting point. Using the analytical solution, predict the resonance point and run a simulation at the resonance point. You might have to run awhile for transients to die away (i.e. consider the homogeneous solution without the driving 1 force and you determine the time). Do the computed amplitude and phase agree with analytical predictions? 2...
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- Fall '08