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Grade 12Mechanics

How is the time period of a spring mass system = 2 pi (disp/accn)^1/2?

Chirag Jain

10 Years agoGrade 12

1 Answer

arun

Approved Tutor Answer10 Years ago

standard equation of S.H.M is

$\frac{\partial^2 x}{\partial t^2} + \omega ^2 x =0$

$a = -\omega ^2 x$

$\left | a\div x \right |= \omega ^2$

$2\pi \div T=\omega$

$T = 2\pi \div \omega$

$T = 2\pi \div \sqrt{\omega ^2}$

$T = 2\pi \div \sqrt{a\div x}$

$T = 2\pi \sqrt{x\div a}$

this means time period of of S.H.M is square root of displacement divided by acceleration.

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