# Damped Harmonic motion

The position x(t) of a mass undergoing damped harmonic motion at an angular frequency ω'
is described by

x(t)=A e^t/τ cos(ώt + delta)

where τ is the time constant, A the initial amplitude and delta an arbitrary phase.

(a) Find an expression for the speed of the mass as it passes through the equilibrium
position.

*Can anyone give me an idea on how to start solving this problem. I havent tried anything because i dont know where to start.

thank you

## Answers and Replies

George Jones
Staff Emeritus
Science Advisor
Gold Member
How do you get velocity from position?

What does "equilibrium" mean?

Equillibrium is the point where all the forces are equal or the stationary point of any system. And the velocity you can find by using: v(t) = -Aw sin(wt + phi) ?

edit: Am i differentiating The function given to find the velocity at any time?

George Jones
Staff Emeritus
Science Advisor
Gold Member
Am i differentiating The function given to find the velocity at any time?

Yes, that is what you should do.

sweet.. thank you