Linearize the pendulum system presented in Lecture 4: i y = I1, I2 sin x + mL2 QU around the equilibrium point corresponding to T = 00. Obtain the torque u which corresponds to the equilibrium point = 00. 1 Ating 1 [m a U(+) au (xas, uc) U(+) [%] te []-[-]- te m eln -9cosx. Sul (240,410) Su(+) O (+)*x x (t) 2 + (+) XS + (+7X ne (((LT), U(+)) [10] [2 T + C+DCVIS 1 / 5- (MIX)) X Linensized equation : 230 2312(0),40(0) = note: The De 11 0 Sin x + 1 u Ye = h te =? 21/1072- |- quest Y(+) *-]. [6] 2 (+) x X (+) ex f(x, u) elwi 1/4 + sevis 76 - 1 Expanded form = , = x Question 2 C Y() = X( (+) lw elw (@='X) ! (ton T+ (50) 80'Cos (60) + I uct) 29='x + (98750). 90 17/01_1 = (+) 336 u corresponding to - [8] + 012 [20507 7-] = (495) (+)30 D can [3] Caz| Junk 10 1 = (+) h = D [8] [2] xe X (+) Torque 2 h(x, u)