Use the worksheet 2mass2springexercise-aperiodic.mw to explore this aperiodic system (no periodic solutions exist). First execute the template example and play with Exploring the graphical consequences of the various paramters in the driven model with damping following these steps in the worksheet. Then insert the new values of the mass spring system and repeat. The Maple worksheet automates all of these steps. You just have to go through and execute the steps.
1) Determine the new equilibrium positions if the second mass is pulled to the right with a constnt unit force per unit mass.
2) Use these as initial conditions to find the resulting motion if the system is released from those positions at rest.
3) Evaluate the amplitudes of the two decoupled modes and the vectors which result from the amplitudes times the corresponding eigenvectors. Plot the rectangle that results from the span of all proper-fraction coefficient linear combinations of the two vectors. [See the worksheet.]
4) Plot your solution together with the rectangle for increasing values of the time, to see it gradually fill that rectangle.
5) Now for the same initial data evaluate the solution with the unit damping factor and repeat. Go through the steps by hand as homework.