Question

Derive the equations of motion of the system shown in the Figure by using Lagrange's equations with x and generalized coordinates. Wu

Answer 1

Given that

the motion of the system shown in figure below

Answer LLLLLL The Generalized co-ordinates in this areano The sinetic energy "t' is caltulated as follows, herreny is the velocity of Pendulum, and 'n" ... is the man as the velocity of the pendulum is given by following equation, vi colat (972603 (0)}}'+colats i sin cousi? o cátisincogój?(1409 COJOJ ilt zil sino jo + Ro? sin? (0) * 720? 208 cm)

nät zal sinto + i? oj 2 Therefore, the kinetit energy equation can be written as follows, T= 1/2 m2 ²+1/2 m (2²+ 2h sino) 6+1262) for small angle osin (0) to which giver, Tolle mi?+112 * Colt 1263) dlat. c 07 /ai]-zmä diat [09/20] » meno a lo2o aloooo the potential energy w' is calculated as, follows. (rassao-1) i Bus + 202 22 - . 12k2²+ mg (8/] for a small angechos .... 1-c0s (0)ą 6/2 . here y is the stiffnes of the spering .. Келе KSIA arbie - Reine

The cagrange eauation are given as follows, 3 dide (ooloilo dilontavlono dlat [ 07 108]- 27100+ evt 20°° subflitute amü for didt Carlondeo for at lan and sa for avlox in ea o oldt Coloi]- allant dulanto ท้ว 1 62 6 substitute inc?ö for aide [all do] eo for an lao and ng is for avido in ea dlat Cor 106] - 07/20 7 0v1 ao 30 mpöt ngco=0 Therefore, The eauation of motion are amat bazo and mi? öt ng 10=of

Answer 2

what is the equation of motion for a system which is given below