First slide

Simple hormonic motion

Question

A particle is executing SHM of amplitude A and time period T along a straight line. Then time required for the particle to directly move from $x = - \frac{A}{\sqrt{2}} to x = + \frac{A}{2} is$

Difficult

A

$\frac{7 T}{24}$
B

$\frac{5 T}{12}$
C

$\frac{7 T}{12}$
D

$\frac{5 T}{24}$

Solution

$∠ POM = \cos^{- 1} (\frac{OM}{OP}) = \cos^{- 1} \frac{A / \sqrt{2}}{A} = \frac{π}{4} ∠ QON = \cos^{- 1} (\frac{ON}{OQ}) = \cos^{- 1} \frac{A / 2}{A} = \frac{π}{3} ∴ ∠ POQ = \frac{π}{4} + \frac{π}{3} = \frac{7 π}{12} π - (\frac{π}{4} + \frac{π}{3}) = π - \frac{7 π}{12} = \frac{5 π}{12} ∴ t = \frac{5 π / 12}{ω} = \frac{5 π / 12}{2 π / T} = \frac{5 T}{24}$

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