Question

(5 points) A spring is suspended vertically from a fixed support. The spring has spring constant k=28 N m−1k=28 N m−1. An object of mass m=14 kgm=14 kg is attached to the bottom of the spring. The subject is subject to damping with damping constant β N m−1 sβ N m−1 s. Let y(t)y(t) be the displacement in metres at the end of the spring below its equilibrium position, at time tt seconds.

(a) Give a value of ββ which would result in underdamping. β=

(5 points) A spring is suspended vertically from a fixed support. The spring has spring constant k- 28 N m 1 An object of mass m- β N m i s Let y t be the displacement in metres at the end ot the spring below its equilbrium position at time t seconds kg is attached to the bottom of the spring. The subject is subject to damping with damping constant (a) Give a value of which would result in underdamping, β- Give your answer as an exact value or as a decima! to at least 3 decimal places. (b) Which of the following plots of yvs. t shows underdamped motion? (c) Give the value of which would result in critical damping β- 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 B 0, for which function(s) F from the list below would resonance occur? Select one or more of the following A.esin(4V7t) B. cos(VTt) C. sin(4VTt) D. 4sin(7i) E. 3 cos(7t) e- F. 5 cos(-4 7t) G.e sin(7t) (e) Which of the following plots of y vs. t show resonance?

Answer 1

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e) option 4 is correct.