Find the expression for time period of motion of a body suspended by two springs connected in parallel and series.
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Two springs in parallel effectively behave as a single spring with spring constant kparallel=k1+k2=2k while two springs in series effectively behave as a single spring with spring constant kseries=k1k2/(k1+k2)=k/2. Recall that the period of a mass on a spring is
T=2πmk−−−√
Which gives
TparallelTseries=kserieskparallel−−−−−−√=k/22k−−−−√=12
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