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Grade 12IIT JEE Entrance Exam

In exams like VITEEE and JEE should motion of shm be considered as Acos(wt) or Asin(wt)?
In a few questions it is not mentioned whether the displacement is considered from the mean position or extreme position. Hence i have this doubt

Profile image of Pranava B
9 Years agoGrade 12
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1 Answer

Profile image of Nitin
9 Years ago
If you start measuring time from the "equilibrium position" then you use Sin.
This is because the sine function is zero at the start when time is zero(Cos is not).
The equilibrium position is zero displacement.

You could use cos if you start time from maximum displacement.

The rule is, if displacement is zero at time zero then use sine.
Sin(0) = 0
Cos(0) = 1

So if you're deciding whether it's sin(wt) or cos(wt) consider what you want happening at t = 0. Often velocity = 0 at t = 0 so the velocity is of the form sin(wt). In the same scenario, there is usually a fixed displacement at t = 0 and so the displacement is of the form cos(wt).

Btw, 'w' should really be 'omega' which is the angular velocity. But my keyboard doesn't have omega. 
 
 

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