Dampening Oscillation Spring Question

[JoeyBob]

Homework Statement

See attached

Relevant Equations

x(t)=Ae^(i(wt+phi))

Since its critically damped that means k/m=(b/2m)^2, which would mean w=ib/2m. So m=ib/w. My issue now is that I need to find work.

I could put w back into x(t) to get Ae^((-b/2m)t+phi). I guess I could make this Acos((-b/2m)t+phi)). But I am kinda lost at this point. Sure, I could find the amplitude but I don't see how to get phi and if I am even approaching the question the right way. I haven't even used the spring constant after all.

The answer is suppose to be 0.614.

 

[JoeyBob]

Ok so w=0 since critically damped, so 0=k-b^2/4m and you solve for m.

 

[mjc123]

On a pedantic point, the word you want is "damping". "Dampening" means "making moist".

 

[kuruman]

My issue now is that I need to find work.

What kind of work are you looking for? Is it work done by the spring on the mass or is it the energy dissipated by the damping force?