two identical springs each of force constant k are connected in series and parallel so that they supports a mass M. find the ratio of the time period of the mass in the two system
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when Spring is connected in parallel
spring factor=k+k=2k
inertia factor=m
time t1=2π√m/2k. ------(i)
when Spring is connected in series
spring factor=k.k/k+k=k/2
time T2=2π√m/k/2
t2=2π√2m/k. ------(ii)
divide (I) by (ii), you get
T1/T2=1/2
spring factor=k+k=2k
inertia factor=m
time t1=2π√m/2k. ------(i)
when Spring is connected in series
spring factor=k.k/k+k=k/2
time T2=2π√m/k/2
t2=2π√2m/k. ------(ii)
divide (I) by (ii), you get
T1/T2=1/2
HimanshuSingh1409:
when you divide 1 and 2 we get 1/root 2
solve equations , there is 1/√2×√2=1/2
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