If a body of mass 36gm moves with S.H.M of amplitude A = 13 cm and period T = 12sec. At a time t = 0 the displacement is x = +13cm. The shortest time of passage from x = +6.5cm to x = – 6.5 is

$\begin{array}{l}\mathrm{A}=13\mathrm{cm},\mathrm{T}=12\mathrm{cm}\\ \text{ time from }+13\mathrm{cm}\text{ to }6.5\mathrm{cm}\\ \mathrm{y}=\mathrm{Acos}\mathrm{\omega t}\\ \Rightarrow \cos \mathrm{\omega t}=\frac{6.5}{13}=\frac{1}{2}=\mathrm{\omega t}=\frac{\mathrm{\pi }}{3}\\ \frac{2\mathrm{\pi }}{\mathrm{T}}\times \mathrm{t}=\frac{\mathrm{\pi }}{3}\Rightarrow \frac{2\mathrm{t}}{\mathrm{T}}\times \frac{1}{3}=\frac{2\mathrm{t}}{12}=\frac{1}{3}\\ \mathrm{t}=\frac{4}{2}=2\sec \end{array}$
From 6.5cm to mean position t₁ = 3 – 2 = 1 sec
From mean position to 6.5cm, $\mathrm{y}=\mathrm{Asin}\mathrm{\omega t}$
$\begin{array}{l}\mathrm{y}=\mathrm{Asin}\left(\frac{2\mathrm{\pi }}{\mathrm{T}}\right)\mathrm{t}\\ \Rightarrow 6.5=13\sin \frac{2\mathrm{\pi }}{\mathrm{T}}\times \mathrm{t}\Rightarrow \frac{\mathrm{\pi }}{6}=\frac{2\mathrm{\pi }}{\mathrm{T}}\times \mathrm{t}\\ \Rightarrow \frac{\mathrm{\pi }}{6}=\frac{2\mathrm{\pi }}{\mathrm{T}}\times \mathrm{t}\Rightarrow \mathrm{t}=\frac{\mathrm{T}}{12}\sec {\mathrm{t}}_2=\frac{12}{12}=1\sec \end{array}$