The transverse vibration of a buckled column under the effect of an external periodic force is described by the ordinary differential equation (ODE) dt 2
d 2
x
​
+β dt
dx
​
−[1+μcos(ωt)]x+x 3
=0,0≤t≤T, where x is the positionn, t is the time, T is the final time, β=0.21 is a damping parameter and the parameters μ=0.29 and ω=1 define the periodic forcing term. The initial value problem is completed with the following initial conditions corresponding to the initial position and the initial velocity x(0)=0 m, dt
dx
​
(0)=v 0
​
m/s (a) Write in the box provided in the next page, all the steps required to transform the second order differential equation into a system of two first-order differential equations.