PHI 203 Final: PHYS 203 Princeton Final2003a
Document Summary
M: (40 pts) a plane pendulum consists of a bob of mass m suspended by a massless rigid rod of length l that is hinged to a sled of mass m . The sled slides without friction on a horizontal rail. Gravity acts with the usual downward acceleration g. g l m: taking x and as generalized coordinates write the lagrangian for the system. X2 = (m + m )/over2 + m. 2 2 xl cos + 2l2 . L = t v = (m + m ) 2 2 xl cos + 2l2 + mgl cos where uninteresting constants have been dropped: use lagrange"s equations to derive the equations of motion for the system. Solution: for x we have and for d dt. = (m + m ) x + ml cos m 2l sin = 0 d dt.
