In situation as shown in figure time period of vertical oscillation of block for small displacements

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13.Oscillations

normal

In the situation as shown in figure time period of vertical oscillation of block for small displacements will be

A

$2\pi \cos \theta \sqrt {\frac{m}{{2k}}} $

B

$2\pi \sec \theta \sqrt {\frac{m}{{2k}}} $

C

$2\pi \sin \theta \sqrt {\frac{m}{{2k}}} $

D

$2\pi \cos ec\theta \sqrt {\frac{m}{{2k}}} $

Solution

Let block be displaced through $x$ in downward

direction and elongation in spring $=\mathrm{x}_{1}$ then

$x \cos \theta=x_{1}$ $…(1)$

Restoring force $\mathrm{F}=2 \mathrm{kx}_{1} \cos \theta$

$\mathrm{F}=2 \mathrm{k} \cos ^{2} \theta \times$

Hence $\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{m}}{2 \mathrm{k} \cos ^{2} \theta}}=2 \pi \sec \theta \sqrt{\frac{\mathrm{m}}{2 \mathrm{k}}}$

Standard 11

Physics

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