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Define periodic time and angular frequency and obtain the relation between them. |
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Answer» Solution :Periodic time : ..The time required to COMPLETE one rotation is called periodic time (T)... Angular frequency : `2pi` time the frequency of an oscillator is called angular frequency `(omega)` `therefore omega = (2pi)/(T)` The displacement of SHM PARTICLE with amplitude A and INITIAL phase `phi=0` at time t is `x(t)= A sin omega t"""........."(1)` Since the MOTION has a period T, hence `x(t)= x(t+T)" That is "A COS omega t= A cos (omega t + phi)"""........."(2)` Now the cosine function is periodic with period `2pi` means phase increase by `2pi` and it motion repeared. `therefore omega t+2pi = omega(t+T)` `therefore omega t+ 2pi = omega t+ omega T` `therefore 2pi = omegaT` `therefore omega = (2pi)/(T)` but `(1)/(T)=v` (frequency) `therefore omega= 2pi v` So `pi" is "2pi` time the frequency of oscillation `v(1/T)`. |
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