is one problem. Thank you.

Let , x = x2 7, =- 12 sinn, be the nonlinear equation of a simple pendulum . a) Where are the equilibrium point of the pendulum? [Tell me where the roh.s. of is zero 6 Linearize in the in the vicinity of (0,0) and write down an equation similar to (9.8). 3=MX What is M? GX ch li) write down the eigenvalues and eigenvectors of m from part 6. (11) Now write down the solution vectors X, (t) and X, it) bor pool for the linear dynamics x=M%. (1) Hence write down the general IN solution (U)= 4,8,0 + 2XU [see (9-17) in the notes choose x,(0)=1, (0) = 1 + 2 , calculate c, and 2 What is the time period of oscillation? e 6 @ Taking the lineer dynamics in part 6 write down the equation of the ellipse Plot this ellipe an indicating the direction of the phase parbrit. [choose xo=1 and play in the value of 9/1 ]