Question

For the critically damped case:

x(t)=(A+B)e^(-bt/2m)

is the general solution to the differential equation. If the critically damped oscillations start at the equilibrium position with a velocity of v_0, determine the maxium displacement of the object......

Please Help... :/

Answer 1

Take the derivative to find velocity as a function of time, making sure that v(0)=v_0. Then you can find the maximum of the position function by setting v(t) that you just found equal to zero, since to find the maximum of a function you take its derivative and let it equal zero. I hope that helps.

Answer 2

Nice

Answer 3

Also, if you think about it, at amplitude the velocity will be zero, since it's changing direction, which fits with maximising the function.