b
Maximum velocity in \(\mathrm{SHM}, \mathrm{v}_{\max }=\mathrm{a} \omega\)
Maximum acceleration in \(\mathrm{SHM}, \mathrm{A}_{\max }=\mathrm{a} \omega^{2}\)
where \(a\) and \(\omega\) are maximum amplitude and angular frequency.
Given that, \(\frac{A_{\max }}{v_{\max }}=10\)
i.e., \(\omega=10 \mathrm{s}^{-1}\)
Displacement is given by

\(x=a \sin (\omega t+\pi t 4)\)
at \(t=0, x=5\)

\(5=a \sin \pi / 4\)

\(5=a \sin 45^{\circ} \Rightarrow a=5 \sqrt{2}\)
Maximum acceleration \(\mathrm{A}_{\mathrm{max}}=\mathrm{a} \omega^{2}\)

\(=500\sqrt{2}\,m/s^2\)