Difficult Trig Word Problem

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?

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  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) )

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  2. sorry

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

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

    4^(-3t) = 0 ----> so solution
    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

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