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A particle of mass 2 kg is moving on a s...

A particle of mass `2 kg` is moving on a straight line under the action of force `F = (8 - 2x)N`. It released at rest from `x = 6 m`.
(a) Is the particle moving simple harmonically.
(b) Find the equilibrium position of the particle.
(c) Write the equation of motionof the particle.
(d) Find the time period of `SHM`.

Text Solution

Verified by Experts

. F = 8 – 2x `" "`or`" "` F = –2(x – 4) for equilibrium position F = 0
`implies" "` x = 4m is equilibrium position. Hence the motion of particle is SHM with force constant 2 and equilibrium position x =4.
(a) Yes, motion is SHM.
(b) Equilibrium position is x = 4m.
(c) At x = 6 m, particle at rest i.e. it is one of the extreme position. Hence amplitude is A = 2 m and initially particle at the extreme position.
`:. " " ` Equation of SHM can be written as x – 4 = 2 cos `omega`t,
where `omega = sqrt((k)/(m))=sqrt((2)/(2))=1 (sec)^(-1)`
i.e x = 4 +2 cos t
(d) Time period T = `(2pi)/(omega) = 2 pi` sec.
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