Question 259: Oscillations

Question

' $P$ ' and ' $Q$ ' are fixed points in same plane and mass ' $m$ ' is tied by string as shown in figure. If the mass is displaced slightly out of this plane and released, it will oscillate with time period $(\mathrm{PQ}=2 \mathrm{~d}, \mathrm{PR}=\mathrm{QR}=\mathrm{L})(\mathrm{g}=$ gravitational acceleration)

Accepted Answer

The motion of mass ' $m$ ' is defined as a simple harmonic motion (S.H.M) with its length equal to OR:
From figure, $\mathrm{OR}=\sqrt{\mathrm{L}^2-\mathrm{d}^2}$
$	herefore \quad$ Time period, $\mathrm{T}=2 \pi \sqrt{\frac{\left(\mathrm{~L}^2-\mathrm{d}^2ight)^{1 / 2}}{\mathrm{~g}}}$

Answer

$2 \pi \sqrt{\frac{\mathrm{~L}}{\mathrm{~g}}}$

Answer

$2 \pi \sqrt{\frac{\mathrm{~L}^2}{\mathrm{~g}}}$

Answer

$2 \pi \sqrt{\frac{\left(L^2-d^2\right)^{1 / 2}}{g}}$

Answer

$2 \pi \sqrt{\frac{\left(L^2+d^2\right)^{1 / 2}}{g}}$

Oscillations

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