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प्रश्न
In SI units, the differential equation of an S.H.M. is `(d^2x)/(dt^2)` = − 36x. Find its frequency and period.
The differential equation of linear S.H.M. in SI units is `(d^2x)/(dt^2)` = − 36x. Calculate its frequency and periodic time.
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उत्तर
`(d^2x)/(dt^2)` = − 36x
Comparing this equation with the general equation,
`(d^2x)/(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
∴ The period,
T = `1/f`
= `1/0.9548`
= 1.047 s
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