A simple pendulum with length L and mass m of bob is vibrating with an amplitude A . maximum t

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13.Oscillations

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A simple pendulum with length $L$ and mass $m$ of the bob is vibrating with an amplitude $A$. The maximum tension in the string is

A

$mg$

B

$mg\left[ {1 + {{\left( {\frac{A}{L}} \right)}^2}} \right]$

C

$mg\left[ {1 + {{\left( {\frac{A}{2L}} \right)}^2}} \right]$

D

$mg\left[ {1 - {{\left( {\frac{3A}{L}} \right)}^2}} \right]$

Solution

$\mathrm{T}_{\max }-\mathrm{mg}=\frac{\mathrm{mv}^{2}}{\mathrm{L}}$

$\mathrm{T}_{\max }=\mathrm{mg}+\frac{\mathrm{m}(\mathrm{A} \omega)^{2}}{\mathrm{L}^{2}}$

$=m g+\frac{m}{L} A^{2} \frac{g}{L}=m g\left[1+\frac{A^{2}}{L^{2}}\right]$

Standard 11

Physics

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