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## Homework Statement

hi im trying out a question on dimensional analysis , im having trouble finding the solution when the force is non linear , the situation is a mass resting on a smooth surface attatched to a spring , the spring is attached to a wall on its other end ,

## Homework Equations

the expression for the non linear force is

[tex] f= -kx + bx^2[/tex]

## The Attempt at a Solution

, what will be the expression for the frequency? [tex]\omega=m^d *k^e* (bx)^f*x^g[/tex]? or maybe not since its not giving me the expected answer. i found the expression for the case when the force is linear [itex]f=-kx[/itex]: [itex]\omega= c \sqrt{k/m}[/itex] , the epected answer for the non linear case is of the form [tex] \omega = f(x_o \frac{b}{k}) \sqrt{k/m} [/tex]