A particle of mass M moves in one dimension along the positive x axis, under the

Question

A particle of mass M moves in one dimension along the positive x axis, under the influence of two forces. The first force is a constant force, with magnitude B and direction toward the origin. The second force is an inverse square law, with magnitude A/x2 and direction away from the origin. Find the potential energy function, and sketch the energy diagram for motion with energy E. Find the equilibrium position.
Calculate the frequency of small oscillations around the equilibrium. [Data: M = 0.63 kg; B = 36 N; A = 37 Nm2.]

F=dU/dx=-B+A/x^2=0 for equilibrium x=1.0138

U=-(Bx^2+A)

What is the relationship between potential and frequency?

Explanation / Answer

F = dU/dx

taking force towards origin to be positive

F = 36 - 37/x2

integrating w.r.t x

U = 36x + 37/x + C

U = 1/2 k A2 where A is the amplitude and frequency = 1/2* (k/m) where m is mass equate k in both relation you will get the required relation. Amplitude will be x=1.0138 as there velocity in zer0

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