From Newton's second law, the displacement y(t) of the mass in a mass,

spring, dashpot system satisfies

m*(d^2y)/dt^2= F_s + F_d, for 0 < t,

where m is the mass, F_s is the restoring force in the spring, and F_d is the

damping force. To have a compete IVP we need to state the initial conditions,

and for this problem assume

y(0) = 0,

dy/dt (0) = v0.

(a) Suppose there is no damping, so F_d = 0, and the spring is linear, so

F_s = ky. What are the dimensions for the spring constant k? Nondi-

mensionalize the resulting IVP. Your choice for y_c and t_c 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,

F_d = c*(dy/dt)

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 Ethat measures the strength of the

damping. In particular, if c is small then Eis small. The system in this

case is said to have weak damping.