X M A B 10 C mvg Problem 6: A mass M travels in a straight...

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X M A B 10 C mvg Problem 6: A mass M travels in a straight line on a horizontal plane block. It is attached at one end to a fixed vertical wall through a spring (spring constant k) while at the other end, it is connected through an inextensible cable to a pendulum of mass m. The lower mass m will oscillate in the vertical plane ABC and there is no friction. Using the position x of the mass M and the angle of the mass m, as the configuration variables, write the two equations of motion. You can use the length of the string connecting the two masses as 1, the unstretched length of spring as lo, and the length of the horizontal plane block in x-direction as t. - Ans: (M + m)x m[g cos 0 + (lo + x l)] + k(x l) = 0 EOM #1 [lo + x l] + 2x + g sin 0 = 0 EOM #2 X M A B 10 C mvg Problem 6: A mass M travels in a straight line on a horizontal plane block. It is attached at one end to a fixed vertical wall through a spring (spring constant k) while at the other end, it is connected through an inextensible cable to a pendulum of mass m. The lower mass m will oscillate in the vertical plane ABC and there is no friction. Using the position x of the mass M and the angle of the mass m, as the configuration variables, write the two equations of motion. You can use the length of the string connecting the two masses as 1, the unstretched length of spring as lo, and the length of the horizontal plane block in x-direction as t. - Ans: (M + m)x m[g cos 0 + (lo + x l)] + k(x l) = 0 EOM #1 [lo + x l] + 2x + g sin 0 = 0 EOM #2