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Question

Two springs of force constants K1 and K2 are connected to a mass m placed on a horizontal frictionless surface as shown in figure. (a) and (b). what is the ratio of the time periods of horizontal oscillation in cases (a) and (b) if K1=K2

A
14
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B
12
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C
2
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D
4
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Solution

The correct option is C 2
In case (a) the springs are connected in series. Therefore, the spring constant of the combination is given by
1k=1k1+1k2=1k+1k=2k (k1=k2=k) Therefore, for case(a),
k=k2
Ta=2πmk=2π2mk
In case (b) the spring constant of the combination is
k′′=k1+k2=2k
Tb=2πmk′′=2πm2k
Thus TaTb=2
Hence the correct choice is (c)

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