Question

A particle of mass `1.5` kg moves along x-axis in a conservative force field. Its potential energy is given by `V(x)=2x^(3)-9x^(2)+12x,` where all quantities are written in SI units. The plot of this potential energy is given below.
It is seen that the particle can be in stable equilibrium at a point on x-axis, x_(0). When it is displaced slightly from this equilibrium position, It executes SHM with time period T. What is the time period of SHM mentioned in the paragraph?
A. `pi sec`
B. `2pi sec`
C. `pi/2 sec`
D. `pi/4 sec`

Answer 1

Correct Answer - A
`a=F=-6(x^(2)-3x+2)`
`a=-4(x^(2)-3x+2)=-4((2+y)^(2)-3(2+y)+2)`
`=-4(4+y^(2)+4y-6-3y+2)`
`a=-4y`
`omega-2`
`T=(2pi)/2=pi sec`