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Problem 2 A spring-mass-damper system oscillating about the horizontal surface is subjected to an external force of F = F, sin wt, where F, is in Newtons and w is in radians per second. The system has a mass m [kg], a damping coefficient of b [N.s/m] and a spring constant of k [N/m]. The system is both given an initial displacement of x, [m] and an initial velocity of vo [m/s] a. Using Method of Undetermined Coefficients, determine the particular solution for the displacement function. [20 pts] b. Determine the unknown coefficients for the homogeneous solution using the initial conditions (Note: the external force already works at t = 0). [20 pts] c. Determine the position, velocity and acceleration of the system after 10 seconds. [10 pts] wie