5. (6 pts pts) The displacement of a spring vibrating in damped harmonic motion is given by
y = 4e-3t sin(2πt)
Find the times when the spring is at its equilibrium position (y = 0). '

The  times when the spring is at its equilibrium position (y = 0) are t = 0, 1/2, 1, 3/2, ... and so on.

To find the times when the spring is at its equilibrium position (y = 0), we can set the displacement equation equal to zero and solve for t:

[tex]4e^{(-3t)[/tex] sin(2πt) = 0

Since the product of two factors is zero if and only if at least one of the factors is zero, we have two cases to consider:

4[tex]e^{(-3t)[/tex] = 0

This equation has no solution since [tex]e^{(-3t)[/tex] is always positive and nonzero.

sin(2πt) = 0

The sine function is zero at integer multiples of π.

So, we can set 2πt equal to integer multiples of π:

2πt = 0, π, 2π, 3π, ...

Solving for t in each case, we get:

t = 0, 1/2, 1, 3/2, ...

Therefore, the times when the spring is at its equilibrium position (y = 0) are t = 0, 1/2, 1, 3/2, ... and so on.

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2x + y = 2
x - y = 1

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The other has a perimeter of 20 inches
Select the two rectangles that could be the rectangles Carla draws
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Х
G
B)
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