Derivatives of Trig Functions: Applications
4. A weight which is connected to a spring moves so that its displacement is:
x = sin 2t + 31/2cos 2t in centimeters.
What is its maximum displacement?
Take the derivative and set it equal to zero.
dx/dt = 2 cos 2t + 31/2 * 2(-sin 2t)
0 = 2 cos 2t – 2*31/2 sin 2t
sin 2t/cos 2t = 1/31/2
tan 2t = 1/31/2
2t = 30o
Plug this into the original equation for x:
xmax = sin (30) + 31/2cos (30) = 2 cm