The motion of a particle performing damped oscillations is given by the formula

Question

y = e-t sin2t

Where y - displacement from its mean position and t - time in seconds


(a)determine the time at which the velocity of the particle is 0

(b)Determine if the displacement of the particle reaches a maximum or a minimum at the time when the velocity is 0

(c)Hence, find the displacement

Answer 1

what's the problem? As usual, take the drivative. y' is the velocity.

y' = -e^-t sin2t + 2e^-t cos2t
= e^-t (sin2t + 2cos2t)

so, velocity=0 when sin2t + 2cos2t = 0
sin2t = -2cos2t
tan2t = -2
so, find arctan(-2) and add multiples of pi/2 to t