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1.	In SI units, the differential equation of an S.H.M. is d2x/dt2 = − 36x. Find its frequency and period.
Answer» \(\frac{d^2x}{dt^2}+\omega^2x = 0\).......(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

In SI units, the differential equation of an S.H.M. is d2x/dt2 = − 36x. Find its frequency and period.

Answer»

\(\frac{d^2x}{dt^2}+\omega^2x = 0\).......(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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