Q.

The time period of vertical oscillations of the system shown in Fig. is  (given k1=k2=k and k3=2k )

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a

2πmk

b

2π3mk

c

2πm3k

d

2π2m3k

answer is A.

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Detailed Solution

The spring constant of the parallel combination of springs of spring constants k1 and k2 iskp=k1+k2=k+k=2kThis combination is in series with the spring of spring constant k3. So the effective spring constant of the system is1keff=1kp+1k3=12k+12k=1k∴ keff=kand T=2πmkeff=2πmkSo the correct choice is (a).
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The time period of vertical oscillations of the system shown in Fig. is  (given k1=k2=k and k3=2k )