The potential energy of a conservative force field is given by `U=ax^(2)-bx` where, a and b are positive constants. Find the equilibrium position and discuss whether the equilibrium is stable, unstable or neutral.
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A, B
In a conservative field `F = -(dU)/(dx)` `:. F=-d/dx(ax^2-bx)=b-2ax` For equilibrinm `F=0` or `b - 2 ax = 0 :. x=b/2_(a)` From the given equation we can see that `(d^(2)U)/(dx^(2))=2a` (positive), i.e. U is minimum. Therefore, `x=b/2a` is the stabele equilibrium position.
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