Let the position of the mass center, G, be measured by a coordinate x that is parallel to the inclined plane and positive down the plane, with origin where the spring is undeterred. Obtain the equation of motion (ODE) that governs the system\'s motion. Solution Resultant spring constant = 2k * k /(2k+k) = 2k/3 Resultant C = 2C/3 Differential force equation is -2k/3 x + 2C/3 x\' + mg = mx\".

1. Let the position of the mass center, G, be measured by a coordinate x that is parallel to the
inclined plane and positive down the plane, with origin where the spring is undeterred. Obtain
the equation of motion (ODE) that governs the system's motion.
Solution
Resultant spring constant = 2k * k /(2k+k) = 2k/3 Resultant C = 2C/3 Differential
force equation is -2k/3 x + 2C/3 x' + mg = mx"