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Question
In SI units, the differential equation of an S.H.M. is `("d"^2"x")/("dt"^2)` = − 36x. Find its frequency and period.
Solution
`("d"^2"x")/("dt"^2)` = − 36x
Comparing this equation with the general equation,
`("d"^2"x")/("dt"^2)` = − ω2x
We get, ω2 = 36 ∴ ω = 6 rad/s
ω = 2πf
∴ The frequency, f = `ω/(2π)=6/(2(3.142))=6/6.284` = 0.9548 Hz
and the period, T = `1/"f"=1/0.9548` = 1.047 s
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