Homework $3$

Given the system in figure, determine the expression:

of the Total Potential Energy expanded up to the $4-$th order terms;

of the in$-$series expanded Equilibrium Equation.

Then, by using the Strained Parameter Method, determine the critical load and the asymptotic expression

of the equilibrium paths. Plot the equilibrium paths and discuss their stability, when:

a$)l=1m,k_e=2k\frac{N}{m},k_f=3kN*m,{}_0=\frac{1}{100}$

b$)l=1m,k_e=1k\frac{N}{m},k_f=4kN*m,{}_0=\frac{1}{100}$

Determine the coordinates of the limit point in the case a$).$