Question

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ed support The Spring has spring constant k 6 N m N m (5 points A spring is suspended vertical An o ect or mass m kg is attached to the botom ofthe spring The sub ect is su with damp ng constant t be the om a ect to dam n s Let displacement in metres at the end of the spring below its cquiorium position, at time t scconds. (a) Ghe a value or β which would resut in underdamping β- Give your answer a8 an exact vaive or as a decimai to af least 3 decimai places (b) which ot the tollowing plots of yvs. shows underdamped motion? (c) Give the value arß which would resuit in critical damping β- Give your answer a8 an exacr vaive or as a decimai to af least 3 decimai places suppose that an external torce ot P t Newton directed downwards is applied to the sp ng. With β 0, tor which tunctions F trom the list below would resonance occur? Select one or more of the tollowng A. cos(v2) B. 6sin(2t) G. 3 cos-3V2) e)Which of the folowing plots of y vs.t show resonance?

Answer 1

For under damypin β dompiy where domping ralio O.S 2V6x L 3 NoTe: This,β, corresponds toて=o.S ; Bub Lender da mping m case dompirg, fhe syatem will vibrate bu with decrease im armplitude with me.

For criical dompln 1- 1 3 β 2.828

wil resonate when external orce natural fre9uureǐ matches with S reque uem Now (F),(G) are possi ble ang wers In vresonance , Arnpkifiude vahior ried to hnfiwity Hernce,
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