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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The position of equilibrium is b/2a and the equilibrium is stable.
Given the potential energy of a conservative force field , U = ax² - bx where a and b are positive constant.
F = -dU/dx = force is equal to the differential of potential energy w.r.t x.
F = -2ax + b
For equilibrium F = 0
=> -2ax + b = 0
=> x = b/2a
d²U/dx² = 2a ( positive as a is a positive constant ), this means that b/2a is point of minima and the equilibrium is stable.
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