In SI units, the differential equation of an S.H.M. is d^2x/dt^2 = − 36x. Find its frequency and period.
In SI units, the differential equation of an S.H.M. is d2x/dt2 = − 36x. Find its frequency and period.
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\(\frac{d^2x}{dt^2}+\omega^2x = 0\).......(i)
\(\frac{d^x}{dt^2} = -36x\)
\(\frac{d^2x}{dt^2}+36x = 0\).....(ii)
\(\omega^2 = 36\)
\(\omega=\sqrt{36}\) = 6 cycles/s
\(\omega\) \(=2\pi n\)
n = \(\frac{\omega}{2\pi}=\frac{3}{\pi}\)\(=\frac{3}{3.14}\) = 0.95 s-1
n = \(\frac1T\)
T = \(\frac1n\) = \(\frac1{0.95}\)
= 1.04 second
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