# Damped harmonic motion question

A damped harmonic motion starts from rest at time t=0 with displacement A0 has the equation:

x(t) = A0/cos (delta)*e^(-t/tau) *cos (w't + delta)

w' is the angular frequency, tau is the time constant and delta is given by:

tan (delta) = - (1/w' tau)

find the time when the maximum negative displacement occurs. express it in terms of period.

So, Can you just give me a hint on where to start and where to go from there.

Thank you

kuruman
Homework Helper
Gold Member
Hint: Which term in your expression for x(t) can conceivably turn negative as time increases? Is it the exponential or is it the cosine?

That would be the exponential since we have -t in there. So i guess in this case i am supposed to differentiate with respect to t first?

kuruman
Homework Helper
Gold Member
Just wait before you take any derivatives.

$$e^{-t}=\frac{1}{e^t}$$

For what value of t is the expression negative?

oh oops i dint see that part. The exponential is going to give me a positive value. How did i forget that. my bad

kuruman
Homework Helper
Gold Member
Do you know where to go from here? The first thing to do is to find a value for the phase delta.

I dont know exactly where to go since i am confused about what it is asking for exactly. And to find the value for delta i will be using the tan (delta) = (1/w' tau) and then i guess i can substitute w' = 2*pi/ T' in there and go from there?

kuruman