A particle located in a one - dimentional potential field has its potential energy functions as U(x) = ax4−bx2, where a and b are positive constants. The positionof equilibrium x corresponds to
The position of equilibrium corresponds to F(x) = 0
so F(x)=ddx(ax4−bx2) or F(x)=4ax5−2bx3
For equilibrium m, F(x) = 0, therefore
Putting x=±√ gives −d2U(x)dx2 as negative
So U is maximum. Hence, it is position of unstable equilibrium.