Please solve part d. Thank you for your help!! An object is attached to the end of a vibrating spring and its displacement from its equilibrium position is y = 8e -t/2 sin 4t , where t is measured in...

Please solve part d. Thank you for your help!!

An object is attached to the end of a vibrating spring and its displacement from its equilibrium position is
y = 8e^-t/2sin 4t, where
t
is measured in seconds and
y
is measured in centimeters.

a. Graph the displacement function together with the functions
y = 8e^-t/2

and
y = -8e^-t/2.
How are these graphs related?

b. Use the graph to estimate the maximum value of the displacement. Explain whether or not it occurs when the graph touches the graph of
y = 8e^-t/2
.

c. What is the velocity of the object when it first returns to its equilibrium position?

d. Use the graph to estimate the time after which the displacement is no more than 2 cm from equilibrium.