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

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

Text Solution

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`F = 8 - 2x `
or `F = -2(x - 4)`
at equilibrium position `F = 0`
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 = 4`
(c) At `x = 6 m`, particle is at rest i.e., it is one of the extreme position Hence amlitude is `A = 2 m` and initially particle is at the extreme position.

`:.` Equation of `SHM` can be written as
`x - 4 = 2 omegat`, where `omega = sqrt((k)/(m)) = sqrt((2)/(2)) = 1`
i.e., `x = 4 + 2 cos t`
(d) Time period, `T = (2pi)/(omega) = 2pisec`.
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