The Energy $~E~$ is
$$E=\frac 12\,v^2+\frac 12\,\omega^2\,s^2+ g\,(\sin(\phi)+\cos(\phi)\,\mu)\,s$$$$E=\frac 12\,v^2+\frac 12\,\omega^2\,s^2- g\,(\sin(\phi)+\cos(\phi)\,\mu)\,s$$
where $~\omega^2=\frac km~$
at $~t=0~$, $E_0=E(v=0~,s=s_0)~$ and at point P ,$~E_P=E(s=d)~$
solve $~E_P=E_0~$ for the velocity $~v~$
$$\boxed{\,v_P^2=\left(s_0^2-d^2\right)\omega^2+ \left(\frac 85+\frac 65\,\mu\right)\,g\,(s_0-d)\,} $$$$\boxed{\,v_P^2=\left(s_0^2-d^2\right)\omega^2+ \left(\frac 85+\frac 65\,\mu\right)\,g\,(d-s_0)\,} $$
with $~\sin(\phi)=\frac 45~,\cos(\phi)=\frac 35$