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Show that the phase difference between displacement and velocity is 90 degree and between the displacement and acceleration is 180 degree

Show that the phase difference between displacement and velocity is 90 degree and between the displacement and acceleration is 180 degree

Grade:12th pass

1 Answers

harini
37 Points
4 years ago
      from the graphs of accelration,velocity and displacemnt(please look for them in your 11th NCERT ;) i couldnt copy, paste the image :/ ) it is evident that velocity lags back displacement by 90 and acceleration leads displacement by 180. you can also verify it using the basic SHM equation x(t)= Acos(wt+@)   for velocity it will be V(t)= -Awsin(wt+@) {by differentitaing displacement equation, this equation of velocity is obtained) similarly differentitiate acceleration , we’ll be getting a(t)= -Aw^2cos(wt+@).this last equation can be again simplified as a(t)= -w^2x(t) clearly depicts acceleration is proportional to displacement but out of phase(180) with displacement and this is the one of the most essential conditions of a particle to be in SHM. 
    Hope it helps :)

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