A weight is attached to a spring suspended vertically from a ceiling. When a driving force is applied to the system, the weight moves vertically from its equilibrium position, and this motion is modeled by y = 1 / 3 sin 2t + 1 /4 cos 2t where y is the displacement (in feet) from equilibrium
of the weight and t is the time (in seconds).
(a) Use the identity a sin BΘ + b cos BΘ = √a2 + b2 sin(BΘ + C) where C = arctan(b / a), a > 0, to write the model in the form y = √a2 + b2 sin(Bt + C).
(b) Find the amplitude of the oscillations of the weight.
(c) Find the frequency of the oscillations of the weight.