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Q.

The differential equation representing the S H M of a particle is $9 \frac{d^{2} y}{d t^{2}} + 4 y = 0$ . The time period of the particle is given by

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a

\frac{π}{3} \sec

b

π \sec

c

3 π \sec

d

\frac{2 π}{3} \sec

answer is D.

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Detailed Solution

9 \frac{d^{2} y}{{dt}^{2}} + 4 y = 0; \frac{d^{2} y}{{dt}^{2}} = \frac{- 4}{9} y ..... (1)

$a = \frac{- 4}{9} y$

$compare with a = - ω^{2} y$

$\Rightarrow ω^{2} = \frac{4}{9}$

$\Rightarrow ω = \frac{2}{3}$

$T = 3 π$

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The differential equation representing the S H M of a particle is 9d2ydt2+4y=0 . The time period of the particle is given by