Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main2004PhysicsOscillationsActual

A particle of mass m is attached to a spring (of spring constant k ) and has a natural angular frequency ₀ . An external force F(t) proportional to t ( ₀ ) is applied to the oscillator. The time displacement of the oscillator will be proportional to

Options

  1. Am ₀^2- ^2
  2. B1 m ( ₀^2- ^2 )
  3. C1 m ( ₀^2+ ^2 )
  4. Dm ₀^2+ ^2

Correct answer

B. 1 m ( ₀^2- ^2 )

Step-by-step solution

For forced oscillations, the displacement is given by x = A ( t + ) with A = F ₀ / m ₀^2- ^2

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 JEE Main PYQs