A block of mass $200\, g$ executing $SHM$ under the influence of a spring of spring constant $K=90\, N\,m^{-1}$ and a damping constant $b=40\, g\,s^{-1}$. The time elapsed for its amplitude to drop to half of its initial value is ...... $s$ (Given $ln\,\frac{1}{2} = -0.693$)
A$7$
B$9$
C$4$
D$11$
Medium
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A$7$
a $\mathrm{X}=\mathrm{X}_{0} \mathrm{e}^{-\left(\frac{\mathrm{b}}{2 \mathrm{m}}\right)t}$
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