The forced damped Duffing equation is given by x''+2x' + x + =fsinrtao Use the harmonic balance method to solve the equation of motion and

The forced damped Duffing equation is given by

x''+2ςx' + x +ε =fsinrtao

Use the harmonic balance method to solve the equation of motion and find the steady state solution. Then solve equation of motion numerically using MATLAB ODE solver ODE45, for initial conditions which are:

x'(0)=0, x(0)=0.85

ξ=0.38

f=0.34+(0.1:0.1:0.5)

r=(0.4:0.4:2.2)

Show the full working out including the MATLAB code.