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Question

Find the time period of the oscillation of mass m in figures.

(i) 2πmk1+k2

(ii) 2πm(k1+k2)k1k2

(iii) 2πm(k1k2)k1k2


A
(x) - (i); (y) - (ii); (z) - (ii)
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B
(x) - (i); (y) - (i); (z) - (ii)
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C
(x) - (ii); (y) - (i); (z) - (iii)
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D
(x) - (i); (y) - (iii); (z) - (ii)
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Solution

The correct option is B (x) - (i); (y) - (i); (z) - (ii)

a) Equivalent spring constant k=k1+k2 (parallel)

T=2πMk=2πmk1+k2

b) Let us, displace the block m towards left through displacement `x'

Resultant force F=F1+F2=(k1+k2)x

Acceleration (F/m)=(k1+k2)xm

Time period T=2πdisplacementAcceleration=2πxx(k1+k2)m=2πmk1+k2

The equivalent spring constant k=k1+k2

c) In series combination, let equivalent spring constant be k.

So, 1k=1k1+1k2=k2+k1k1k2 k=k1k2k1+k2

T=2πMk=2πm(k1+k2)k1k2


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