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two identical spring each of force constant K are contected in 1) series

2)parallel so that they support a mass m. find the ratio of the time periods of the mass in the two system

Asked by futureisbright051101 3rd March 2018, 8:09 PM
Answered by Expert
Answer:
begin mathsize 12px style T subscript S space colon space T subscript p space equals space square root of 2 space colon space fraction numerator 1 over denominator square root of 2 end fraction space equals space 2 space colon space 1 end style
when two identical spring each having force constant K are connected in series, then the effective force constant is K+K = 2K;
 
Time period of series combination: Ts  begin mathsize 12px style equals space 2 pi square root of fraction numerator open parentheses 2 K close parentheses over denominator m end fraction end root end style
 
when two identical spring each having force constant K are connected in parallel, then the effective force constant is K/2;
 
Time period of parallel combination: Tp  begin mathsize 12px style equals space 2 pi square root of fraction numerator K over denominator 2 m end fraction end root end style
Ratio begin mathsize 12px style T subscript s space colon space T subscript p space equals space square root of 2 space colon space fraction numerator 1 over denominator square root of 2 end fraction space equals space 2 space colon space 1 end style
Answered by Expert 4th March 2018, 4:29 PM
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