Answer Happy

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 2 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 = 2 * mx + 2 + 10 2 1 D= Må? + 5 m( + €0)? + + 278 2 ci? 1 (1-3 02 V= kx² + mgl (1 2 where X and 0 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)?
M k f(t) с m, ī 21 8
(M + m)ä + (i + mé2)+ ci + kx - mgť = f(t) Mä + ci + kx = f(t) jë + młž + ml?ö + cx – mgť @ = 0 Të + młä + mt ö – mgee = 0 jë + młž + mlö – mgť o = 0 M+ Meb + cx + bx = 0 jë + ml2Ö + ci – mgle = {f(t) - Të + ml?ő – mgl 0 = 0