Derive en expenssion of time period …
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Posted by Harshita Narware 1 year, 10 months ago
- 1 answers
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Preeti Dabral 1 year, 10 months ago
Time period T= time required to complete one oscillation.
At equilibrium T0=mg.
For small displacement θ
Restoring force =−mgsinθ
for small θ sinθ≈θ
{tex}\begin{aligned} & \Rightarrow \mathrm{fe}=-\operatorname{mg} \theta=-\mathrm{mg}\left(\frac{\mathrm{x}}{\mathrm{l}}\right) \\ & \text { acceleration } \mathrm{a}=\frac{\mathrm{fe}}{\mathrm{m}}=\frac{-\mathrm{g}}{1} \cdot \mathrm{x} \end{aligned}{/tex}
We know for SHM, a=−w2x
{tex}\begin{aligned} & \Rightarrow \text { On comparing we get } \mathrm{w}=\sqrt{\frac{\mathrm{g}}{\mathrm{l}}} \\ & \therefore \text { Time period of oscillation } \mathrm{T}=\frac{2 \Pi}{\mathrm{w}}=2 \Pi \sqrt{\frac{1}{\mathrm{~g}}} \end{aligned}{/tex}
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