Question

Define Equation of Motion, Natural frequencies, and Mode Shape System of this diagram

ki k2 w M C C1 0 C2 OL m

Answer 1

The equation of motion conists of The pendulam ne I I a hall , memass) hanging from the massi ess string of Length (2) and fixed at a pivot.M. when displaied to an initial angle and released, o the pendulun will soi ng baik forth wstis periodic motion By applying Newsoni second law for rotational system e The motion of quation of the pendulun may as follows. obtained

WWW Exteme point OY 0 ing code Extreme point midpoint ingsing mg coneiden this al a simple pendulani as the hige is Aned. ühle Vitration which neglected so Reaction forces F = ng sine Newlon second Taw F = ma (0 evaluate ® we gen. ang sino sino sino ro ego ama ma g

(1) - go a scal2 n Coorn -go Acceleration from ean - concider n e n -corn - g w 2 g e egle 2 TT [w: ① and ② Go from egration 1971 2T ㅜ Volg OTT і не when we require linear appromination equations from partcas for motion of the. from its verticall up position sinal mohon arould a pendulum. from equation 0 and gaine g sint + 3 x 6
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