(1) To find the external force, the expression of acceleration is required first, and then the form of force is found according to Newton's second law.

V=kx

So the acceleration a=dv/dt= (dv/dx)(dx/dt)

dv/dx=k dx/dt=v

So a=kv

Then F=ma = mkv.

(2) v=dx/dt=kx

Separation variable: (dx)/x=kdt

Integral: lnx=kt+C is substituted into the initial condition: t=0 x=x0, and the solution is: C=lnx0.

So: ln(x/x0)=kt.

When x=x 1, t = [ln (x1/x0)]/k.