Answer the following questions. Be sure to show your work. 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 sin2t + 1/4 cos2t
where y is the distance from equilibrium (in feet) aud t is the time (in seconds).
(a) Use the identity
a . sin B theta + b . cos B theta = (a^2 + b^2)^1/2 . sin(B theta + C)
where C = arctan(b/a), a > 0,
to write the model in the form y = (a^2 + b^2)^1/2 sin(Bt+C).
(b) Find the amplitude of the oscillatious of the weight.
(c) Find the frequency of the oscillations of the weight.