Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main2018PhysicsOscillationsActual

A body of mass M and charge q is connected to a spring of spring constant k . It is oscillating along x -direction about its equilibrium position in the horizontal plane, taken to be at x = 0 , with an amplitude A . An electric field E is applied along the x -direction. Which of the following statements is correct?

Options

  1. AThe total energy of the system is 1 2 m ω 2 A 2 + 1 2 q 2 E 2 k
  2. BThe new equilibrium position is at a distance 2 q E k from x = 0
  3. CThe new equilibrium position is at a distance q E 2 k from x = 0
  4. DThe total energy of the system is 1 2 m ω 2 A 2 - 1 2 q 2 E 2 k .

Correct answer

A. The total energy of the system is 1 2 m ω 2 A 2 + 1 2 q 2 E 2 k

Step-by-step solution

The equilibrium position will shift to a point where the resultant force is equal to zero. k x e q = q E     ⇒ x e q = q E k . Energy = 1 2 m ω 2 A 2 + q E k 2 = 1 2 m ω 2 A 2 + 1 2 q 2 E 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 JEE Main PYQs