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Please HELP!!! Differentiate and apply the Product rule.

Hi there,

I have the following equation to determine the performance properties of a damper (shock absorber).

d(t) = -5e^-5t cos(10t)

u = -5 x 10^-5t

du/dx = 25 x 10^-5t

v = cos(10t)

dv/dx = -10 sin(10t)

Using the given Product rule equation, is applied to the first derivative:

d(uv)/dx = u/dv/dx + v/du/dx

Therefore

d(uv)/dx = 25 x 10^-5t x cos(10t) + -10 sin(10t) x -5 x 10^-5t

= 25 x 10^-5t (cos(10t) + 2 sin(10t))

0 = cos(10t) + 2 sin(10t)

0 = tan(10t) = -1/2

I have attached the model showing measured and modelled deflection for a given damper (shock).

Now I need to answer the following questions; can anyone help....

a) Can anyone explain how I determine the velocity of the rod as it passes the rest position? (please refer to attached graph).

b) how far the rod moves below the rest position after first rebound (dm)? (please refer to attached graph).

Thanks in advanced.