Question

4. (15 pts) Spring k3 is connected to the mid point of the rod and the static equilibrium line is the horizontal line. Write the equations of motion in terms of the absolute motion of the mass c(t) (use up as positive) and the rotation of the rod 0(t) (use clockwise as positive). Please put the results in matrix form. Recall that for a uniform rod Ic.g. = 1 ML. IMPORTANT NOTE: • Using the energy technique: full credit • Using Newton's laws, 2/3 credit! MASS OF ROD - M LENGTH OF ROD - LK L/2 L/2 Lwowie

Answer 1

doondi trao on mass of nod=my length of rod = 1 Сотреде) би яг fne — 14). Tim OS Dsing energy techanique: t u tto otential Energy in Springs - E = 1 K 212 Car I kg 42 Eget klo)? E = kg 1282 Io = moment of inestia of rod about hinged point Tor M22 sulor ober Kinetic energy in massim, a rok = 1 m, (26) 2 Kinetic Energy in rotation 20 d 2 KE, = { to (0) EmEg2.

Total Energy in system = (T.E). TEE E , & Ez + E + Kit, & KIEL 들리라 나일토리라들5024일계와 전놓m군 here system is conservative then TE es const. (27.09.-01 20.03 - ,249 838) + f. (2 32 32) +4; 12(200) + 6 mi (2 zè ii) + 4 mi@). o sin + kr + 1 kg 120+ m, ze + 1 me 0] To - (14 tez E9D of orotim kez 1²0 + m, ut 1 mio here = an O= do dt 0=20 Egr of motion in marmateix form. +2- (m, o Lo Tzel, kirka o n Lo Lo ſ 13 2 / Lo