(5 points) A spring is suspended vertically from a fixed support. The spring has spring constant k = 40 N m¯¹. An object of mass m = ½ kg is attached to the bottom of the spring. The subject is subject to damping with damping constant ẞ N m¹ s. Let y(t) be the displacement in metres at the end of the spring below its equilibrium position, at time t seconds. (a) Give a value of ẞ which would result in underdamping. ẞ = 4 Give your answer as an exact value or as a decimal to at least 3 decimal places. (b) Which of the following plots of y vs. t shows underdamped motion? ТУ ни (c) Give the value of ẞ which would result in critical damping. ẞ= 4*sqrt(2) Give your answer as an exact value or as a decimal to at least 3 decimal places. (d) Suppose that an external force of F(t) Newton directed downwards is applied to the spring. With ẞ = 0, for which function(s) F from the list below would resonance occur? Select one or more of the following: A. 5 cos(-5√√81) B. sin(5√√/81) C. 4 cos(√√81) + e ✓ D. cos(√81) E. e* sin(√81) ✔F. 2 sin(√81) G. et sin(5√√/81) (e) Which of the following plots of y vs. t show resonance? M t Note: In order to get credit for this problem all answers must be correct.