2. с m F(t) k FIGURE Q2 Consider the forced-mass-spring-damper system, as shown on FIGURE Q2. The spring exerts force on the mass in accordance to Hooke's Law. From Newton's Second Law, the displacement of the mass from its rest position, x(t) satisfies the following equation m d²x dx +c- + kx = F(t) dt² dt where m is the mass, k is the spring constant, c is the damping coefficient which is always positive and F(t) is the external force. The motions of force- mass-spring-damper system models depend on whether c² - 4mk > 0, c² 4mk = 0 or c² - 4mk < 0. Given that F(t) = 2 cos(5t) and, value of m and k satisfy the following relations 10 ≤m ≤ 20 and 50 ≤ k ≤70, respectively. a. Construct TWO (2) different force-mass-spring-damper system models for the displacement of the mass, x(t) and solve the models with initial conditions x(0) = 2 and x'(0) = 0 by using any appropriate method (choose a value of m and k from the given intervals, respectively for both models). b. [20 marks] From your results in Q2(a), discuss the behaviour of the mass displacement, x(t) for the interval of 0 ≤t ≤ 5. [10 marks]