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

Question

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, 2 π 2 m k, 2 π m 2 k, 2 π m k, 2 π m 3 k

MARKS App · 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. F net = F A + F B cos 45 ° + F C cos 45 ° = ky + 2 ky ′ cos 45 ° = ky + 2 k ycos 45 ° cos 45 ° = 2 ky Also F net = k ′ y ⇒ k ′ y = 2 ky ⇒ k ′ = 2 k T = 2 π m k ′ = 2 π m 2 k

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