The displacement of a spring vibrating in damped harmonic mo

The displacement of a spring vibrating in damped harmonic motion is given by the following equation. Find the first four times when the spring is at its equilibrium position, y = 0, and starting at time t = 0. (Enter your answers as a comma-separated list.)

y = 2 e^6t sin(2t)

t =  

Solution

y = 2 e^6t sin(2t)

2 e^6t sin(2t) =0

e^-6t =0 ( does not exist)

So, sin(2pit) =0

2pit = pi*k ; t = pi*k/2pi = k/2

t = k/2 ;

k = 0,1,2,3 ; t = 0, 1/2 , 1 , 3/2 .... (equilibrium position)