Question

The displacement of a spring vibrating in damped harmonic motion is given by y(t) = 4e^-3t sin(2pi*t) where y = displacement and t = time with t greater than/equal to zero. Find the time(s) when the spring is at its equilibrium position (y=0). The number "e" is Euler's number.

I have absolutely no clue what this is even asking. I have written down the information minus the extra words but I am completely lost. Please help?

Answer 1

I am not sure what the exponent is
the way you typed it using no brackets, it would be
(4e^-3) * tsin(2πt)
or is it
4e^( -3tsin(2πt) )

Answer 2

sorry

y(t) =4e(then the exponent -3t) all times sin(2pi*t)

Answer 3

y = 4^(-3t) * sin(2πt)
so if we set y = 0

4^(-3t) = 0 ----> so solution
or
sin(2πt) = 0
2πt = 0 or 2πt = π or 2πt = 2π or ..
t = 0 or t = 1/2 or t = 1 or t= ..
looks like every half second, starting with t = 0