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A particle of mass m is attached to three identical springs A, B and C each of force constant k a shown in figure. If the particle of mass m is pushed slightly against the spring A and released then the time period of oscillations is
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Correct option is B
When the particle of mass m at O is pushed by y in the direction of A The spring A will be compressed by y while spring B and C will be stretched by y'=ycos45°. So that the total restoring force on the mass m along OA.Fnet=FA+FBcos45°+FCcos45°=ky+2ky'cos45°=ky+2k(ycos45°)cos45°=2kyAlso Fnet=k'y⇒k'y=2ky⇒k'=2kT=2πmk'=2πm2k
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An ideal spring with spring-constant K is hung from the ceiling and a block of mass M is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum extension in the spring is
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