\(\mathrm{a}=\mathrm{g} \sin \theta\)

\(\ell=\frac{1}{2}(\mathrm{~g} \sin \theta) \mathrm{t}_1^2\)

\(\mathrm{t}_1=\sqrt{\frac{2 \ell}{\mathrm{g} \sin \theta}}\)

Case-\(2\) : With friction

\(a=g \sin \theta-\mu g \cos \theta\)

\(\ell=\frac{1}{2}(g \sin \theta-\mu g \cos \theta) t_2^2\)

\(\sqrt{\frac{2 \ell}{g \sin \theta-\mu g \cos \theta}}=n \sqrt{\frac{2 \ell}{g \sin \theta}}\)

\(\mu=1-\frac{1}{n^2}\)