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derive the time period of oscillation of a pendulum and spring and show that osillation are simple hormonic

derive the time period of oscillation of a pendulum and spring and show that osillation are simple hormonic

Grade:11

1 Answers

Abhinav
askIITians Faculty 387 Points
7 years ago
write the energy equation spring at X extention and mass m velocity v
i.e.
\frac{1}{2}mv^{2}+\frac{1}{2}kx^{2}= constant

differentiating both sides w.r.t dt
we get
mva + kvx = 0

i.e.
a = -\frac{k}{m}x

hence spring mass system is simple hormonic in nature

and
\omega ^{2}=\frac{4\pi }{T^{2}}^{2}=\frac{k}{m}
thus
timeperiod =2\pi \sqrt{\frac{m}{k}}

similarly proceding for pendulum one can get answer


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