Starting from the differential equation for a 1-degree of freedom system with mass m, damping c and spring stiffness a: a- show that the particular solution for the equation with an applied force f, cos(or). ie., mx+cx+x-f, cos(or) can be expressed as x t)-a, cos(or)+a^ sin(wt) and find the values of al and a2 that solve the differential equation in terms of m, c, k and . 5 points. b. use the result from part a to find the value of frequency co of the applied force that maximizes the amplitude of the oscillations of the forced response and show that the value differs from the natural frequency of the undamped system by a term that is equal to one when c-0. 5 points. c- use the results from part a to find an expression for the load transmitted to the foundation ct+kx and find an expression for its maximum value in terms of m, c, k and deduce that expression from the given solution for the vibrations of the system and express the final result using the non-dimensional variables r and defined in the lab 5 handout.