Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 2004
Exam
JEE Main
Year
2004
Subject
Physics
Chapter
Oscillations

JEE Main 2004 · Physics · Oscillations

A particle of mass m is attached to a spring (of spring constant k...

A particle of mass mm is attached to a spring (of spring constant kk ) and has a natural angular frequency ω0\omega_0. An external force F(t)F(t) proportional to $\cos \omega t\left(\omega \neq \omega_0\right) is applied to the oscillator. The time displacement of the oscillator will be proportional to

Options

  1. Amω02−ω2\frac{\mathrm{m}}{\omega_0^2-\omega^2}
  2. B\frac{1}{m\left(\omega_0^2-\omega^2\right)}
  3. C\frac{1}{m\left(\omega_0^2+\omega^2\right)}
  4. Dmω02+ω2\frac{m}{\omega_0^2+\omega^2}

Correct answer

B. \frac{1}{m\left(\omega_0^2-\omega^2\right)}

Step-by-step solution

For forced oscillations, the displacement is given by x=Asin⁡(ωt+ϕ) with A=F0/mω02−ω2\mathrm{x}=\mathrm{A} \sin (\omega \mathrm{t}+\phi) \text{ with } \mathrm{A}=\frac{\mathrm{F}_0 / \mathrm{m}}{\omega_0^2-\omega^2}
Practice Oscillations on Quantrex Academy →

More from Oscillations

A tank contains two immiscible liquids of densities 6ρ and 2ρ . The higher density liquid… JEE Advanced 2026The frequency of oscillation of a mass m suspended by a spring is v_1 . If the length of… JEE Main 2026A spring stretches by 2 mm when it is loaded with a mass of 200 g. From equilibrium… JEE Main 2026A particle is executing simple harmonic motion. Its amplitude is A and time period is 5… JEE Main 2026Match List-I with List-II. List-I List-II A. ^2 ω t I. Periodic with time period T =… JEE Main 2026A uniform disc of radius R and mass M is free to oscillate about the axis A as shown in… JEE Main 2026The velocity of a particle executing simple harmonic motion along x -axis is described as… JEE Main 2026The equation of motion of a particle is given by x = a (50t + (π)/(3)) cm. The particle… JEE Main 2026 Full Oscillations list All JEE Main PYQs