Can you please provide the solution for question 7? This is a practice exam and I would like to know how to solve the problem. Not an academic integrity issue violation

3. For the following, choose the best description of the system from the following: Simple Harmonic Motion (SHM) Overdamped (OD) Underdamped (UD) Critically Damped (CD) Beating (B) Resonant (R) Steady-State plus Transient (S ST) 3. y\" + 43/ = 0 b. y\" + (1.8)2y = cos(2t) c. y\" + 4)! = cos(2t) d. y\" + y' + y = 0 e. y\" + y' + y = c0505) f. y\"+2y'+y=0 4. The motion of a force mass-spring system is described by the following IVP: u\" + 9n = cos(3t), u(0) = 0, u'(0) = 0 (a) Explain why you expect resonance to occur. (b) Solve this WP and sketch the graph of the solution. 5. The motion of a force mass-spring system is described by the following IVP: u" + (2.8)211 = cos(3t), 11(0) 2 0, u'(0) = 0 Explain why you expect the beats phenomenon to occur. (3) Explain why you expect resonance to occur. (b) Solve this IVP and write your solution in the form A sin(at) sintt). (c) Determine the length of the beats and the period of the oscillation. 6. A mass m = 1 is attached to a sprin g with constant k = 2 and damping constant 1/. Determine the value of 1: so that the motion is critically damped. 7. The position function of a mass-spring system satisfies the differential equation mx\" + yx' + kx : cos(mt), 13(0) : 0, x'(0) : 0. Assumem = 1 and k = 9. [fy at 0, the amplitude of the forced oscillation is given by C = J; (9m2)2 +1,sz Assume y = 1. Differentiate C to find the value of a; at which practical resonance occurs. Determine the corresponding value of C. V. Laplace Transform 1. Use the denition of the Laplace transform to find 17(5) = .I {f (15)] for the following functions. (a)f