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  4. Two light strings, each of length l, are fixed at points A and B on a fixed horizontal rod x y. A small bob is tied by both strings and in equilibrium, the strings are making angle 45° with the rod. If the bob is slightly displaced normal to the plane of the strings and released then period of the resulting small oscillation will be: <img class=img-fluid question-image alt=image src=https://cdn.tardigrade.in/img/question/physics/f38277cea3c4d55fd07c8649093ab992-.png />

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Q. Two light strings, each of length $l$, are fixed at points $A$ and $B$ on a fixed horizontal rod $x y$. A small bob is tied by both strings and in equilibrium, the strings are making angle $45^{\circ}$ with the rod. If the bob is slightly displaced normal to the plane of the strings and released then period of the resulting small oscillation will be :
image

Oscillations

Solution:

In given situation if we look at pendulum from
side its effective oscillating length is $\frac{l}{\sqrt{2}}$
image
Side view of pendulum
Thus angular frequency of oscillations is
$ \omega=\sqrt{\frac{g}{l_{e f f}}}=\sqrt{\frac{\sqrt{2} g}{l}} $
$\Rightarrow T=2 \pi \sqrt{\frac{1}{\sqrt{2} g}}$