Consider the mass-spring system, with mass m in units of slugs, a damping coefficient of 0.50 lb-s/ft, and driven by a periodic external force, 3cos(2t) lb.

my"(t) + 0.50y (t) + ky(t) = 3 cos(2t).

(a) If a mass weighing 8lb stretches the spring 6 inches, determine the model's spring constant k in units of lb/ft.

(b) Using the value of k determined in (a) and leaving m as an unspecified parameter, use undetermined coefficients to find the forced (steady-state) solution in the form

y _p (t) = c ₁ cos(2t) + c ₂ sin(2t). The results for c ₁ and c ₂ will be expressed as functions of the mass M.

(c) From the result in (b), determine the mass m for which the amplitude of the steady-state response is maximum.