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13.Oscillations
hard
Initially system is in equilibrium. Time period of $SHM$ of block in vertical direction is
A
$2\pi \sqrt {\frac{m}{{3k}}} $
B
$2\pi \sqrt {\frac{m}{{2k}}} $
C
$2\pi \sqrt {\frac{m}{k}} $
D
$2\pi \sqrt {\frac{{2m}}{k}} $
Solution
Net vertical force
$=\mathrm{kx}+\frac{\mathrm{kx}}{\sqrt{2}} \cos 45 \times 2=2 \mathrm{kx}=\mathrm{ma}$
$\mathrm{a}=\frac{2 \mathrm{k}}{\mathrm{m}} \mathrm{x}$
$\Rightarrow \omega=\sqrt{\frac{2 \mathrm{k}}{\mathrm{m}}}$
$\tau=2 \pi \sqrt{\frac{\mathrm{m}}{2 \mathrm{k}}}$
Standard 11
Physics
