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=1/3sin2t+1/4cos2t
y=1/3sin2t+1/4cos2t
where y is the distance from equilibrium (in feet) and t is the time (in seconds). Use the identity
asin Bθ + b cosBθ = √a^2+b^2 sin(Bθ+C)
asinBθ+bcosBθ=√a 2
+b 2
sin(Bθ+C)
where C = arctan (b/a), a > 0, to write the model in the form
y=√a^2+b^2 sin(Bt+C)
y=√a 2
+b 2
sin(Bt+C)