Have dv/dx need to find dx/dt ? (have velocity w/ respect displace - find Accel?)

Hi all,

I'm trying to figure out this problem related to motion of a spring. I know the solution but I don't know how to make it work.

Thanks in advance (Nod)

I'm given velocity (v) = where 'x' is displacement

Normally velocity is a function of time, so this one has really thrown me.

I want to find a formula for Acceleration which would normally be quite easy, but the above formula is Velocity as a function of x.

I've done a bit of related rates & differentiating w/ respect other variables, but I can't figure that out for this one....

If Acceleration = = x

and I know (by differentiating the provided equation: --->

then how do I find please?

(btw, using trial and error on my graphics calculator, I think the Acceleration in this case is actually inverse to the displacement).