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(i) The acceleration (a) of a particle m...

(i) The acceleration (a) of a particle moving along a straight line is related to time (t) as per the differential equation `(d^(2)a)/(dt^(2))=-ba.` b is a positive constant. Is the particle performing SHM? If yes, what is the time period?
(ii) A particle is executing SHM on a straight line. A and B are two points at which its velocity is zero. It passes through a certain point P `(AP gt PB)` with a speed of `3 m//s` at times recorded as t = 0, 0.5 s, 2.0 s, 2.5 s, 4.0 s, 4.5 s......Determine the maximum speed of the particle and also the ratio `AP//PB`.

Text Solution

Verified by Experts

The correct Answer is:
`(i) T=(2pi)/(sqrt(b))`
`(ii) V_(Max)=3sqrt(2) m//s. AP//BP=(sqrt(2)-1)//(sqrt()+1)`
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