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Question

# Find the time period of the oscillation of mass m in figures. (i) 2π√mk1+k2 (ii) 2π√m(k1+k2)k1k2 (iii) 2π√m(k1−k2)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=2π√Mk=2π√mk1+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=2π√displacementAcceleration=2π√xx(k1+k2)m=2π√mk1+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=2π√Mk=2π√m(k1+k2)k1k2

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