From Newton's second law, the displacement y(t) of the mass in a mass, spring, dashpot system satisfies d²y m dt2 = F, + Fa, where m is the mass, F, is the restoring force in the spring, and Fa is the damping force. To have a compete IVP we need to state the initial conditions, and for this problem assume dy y(0) = 0, (0) = Vo - dt (a) Suppose there is no damping, so Fa= 0, and the spring is linear, so F; = -ky. What are the dimensions for the spring constant k? Nondimensionalize the resulting IVP. Your choice for y, and to should result in no dimensionless products being left in the IVP. (b)Now, in addition to a linear spring, suppose linear damping is included, so, dy dt Fa What are the dimensions for the damping constant c? Using the same scaling as in part (a), nondimensionalize the IVP. Your answer should contain a dimensionless parameter e that measures the strength of the damping. In particular, if c is small, then e is small. The system in this case is said to have weak damping.

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