Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NTA Abhyas JEE Main2020PhysicsOscillationsPractice

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

Options

  1. A2 π 2 m k
  2. B2 π m 2 k
  3. C2 π m k
  4. D2 π m 3 k

Correct answer

B. 2 π m 2 k

Step-by-step solution

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

Practice Oscillations on Quantrex Academy →

More from Oscillations

A tank contains two immiscible liquids of densities 6 and 2 . The higher density liquid is filled up to a height L/2 from the bottom. A thin rod of density and length L is fully im 2026The frequency of oscillation of a mass m suspended by a spring is v₁ . If the length of the spring is cut to half, the same mass oscillates with frequency v₂ . The value of v₂/v₁ i 2026A spring stretches by 2 mm when it is loaded with a mass of 200 g. From equilibrium position the mass is further pulled down by 2 mm and released. The frequency associated with the 2026A particle is executing simple harmonic motion. Its amplitude is A and time period is 5 sec. The time required by it to move from x = A to x = A 2 is _______ sec. 2026Match List-I with List-II. List-I List-II A. ^2 t I. Periodic with time period T = but not simple harmonic motion (SHM) B. ^3(2 t) II. Periodic with time period T = 2 but Not SHM C 2026A uniform disc of radius R and mass M is free to oscillate about the axis A as shown in the figure. For small oscillations the time period is ______. ( g is acceleration due to gra 2026The velocity of a particle executing simple harmonic motion along x -axis is described as v^2 = 50 - x^2 , where x represents displacement. If the time period of motion is x 7 s, t 2026The equation of motion of a particle is given by x = a (50t + 3 ) cm. The particle will come to rest at time t₁ and it will have zero acceleration at time t₂ . The t₁ and t₂ respec 2026 Full Oscillations list All NTA Abhyas JEE Main PYQs