A particle of mass m is attached to three identical springs A, B and C each of force constant k as 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

Question

A particle of mass m is attached to three identical springs A, B and C each of force constant k as 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

Infinity Learn · Accepted Answer

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′$$=ycos$$⁡$$45$$∘. So that the total restoring force on the mass m along OA. Fnet $$=FA+FBcos$$⁡$$45$$∘$$+FCcos$$⁡$$45$$∘$$=ky+2ky$$′$$cos$$⁡$$45$$∘$$=ky+2kycos$$⁡$$45$$∘$$cos$$⁡$$45$$∘$$=2kyAlso$$ Fnet $$=k$$′y⇒k′$$y=2ky$$⇒k′$$=2kT=2$$$$π$$mk′$$=2$$$$π$$$$m2k$$

A particle of mass m is attached to three identical springs A, B and C each of force constant k as 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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