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In the system shown, a cart of mass M slides on a horizontal surface with viscous friction of coefficient c. It is also attached to ground through a spring of stiffness k and has an external force f(t) applied as shown. A pendulum of mass m, mass moment of inertia (about its centre of mass) I and length 2ť pivots on the cart without friction. The kinetic energy, dissipation function and potential energy of the system shown have been obtained as follows: 1 1 T= m(x + €0)2 + 10 2 2 2 1 D 2 1 V= kx² + mg 2 Mx + 5 ( Col? +370 ci? (1-3 02 where X and are the coordinates chosen to represent the system's motion. Which of the following is a valid equation of motion for the system (there is only one valid answer)?
6 M k www f(t) с m, ī + - 21 8
(M + m)i + (7 + m2)+ cx + kx – mgt = f(t) Mä + ci + kx = f(t) jë + ml x + ml?ë + cả – mgle = 0 jë + młä + mt ö – mgle = 0 Të + mlč + ml2ä - mgle = 0 Mä + MCÖ + cx + kx = 0 jë + mé27 + ci – mgle = tf(t) - jë + me?ö – mgle = 0 -