JEE Main · PhysicsHard
A particle of mass $m$ is attached to a spring of force constant $k$ and performs simple harmonic motion. If the particle is subjected to a damping force proportional to its velocity with damping constant $b$, and an external driving force $F(t) = F_0 \cos(\omega t)$ is applied, what is the phase difference between the displacement and the driving force at resonance?
- A.$0$
- B.$\pi/4$
- C.$\pi/2$
- D.$\pi$
Show correct answer & step-by-step solution
Correct answer: C — $\pi/2$
Solution
At resonance, the driving frequency equals the natural frequency . In a driven damped oscillator, the velocity is in phase with the driving force, and since displacement lags velocity by , the phase difference is .
Attempt this question & track your score
Sign up free to answer, get instant scoring, and let SolveGini track which Physics topics you need to revise.
Attempt & Track Free →More Oscillations & Waves practice questions
- A particle executes simple harmonic motion with an amplitude of 5 cm and a time period of 2 seconds. What is the maximum
- A simple pendulum has a length of 1 meter. What is its approximate time period of oscillation on Earth where g is 9.8 me
- A wave is represented by the equation y = 0.5 sin(10t - 2x). What is the angular frequency of the wave?
- In a spring-mass system, if the mass is doubled while the spring constant remains the same, how does the time period cha
- Which of the following quantities remains constant for a particle executing simple harmonic motion?
- A particle executes simple harmonic motion with an amplitude of 4 cm. At what displacement from the mean position is its
- A simple pendulum has a time period of 4 seconds on Earth. If it is taken to a planet where the acceleration due to grav
- A transverse wave is described by the equation y equals 0.05 sin(2x minus 4t). What is the wave speed?
- Two springs of force constants k1 and k2 are connected in series. What is the effective force constant of the combinatio
- A particle is performing simple harmonic motion with frequency f. What is the frequency of its kinetic energy oscillatio
- A uniform rod of length Land mass M is pivoted at one end and oscillates as a physical pendulum. A small bead of mass m
- A transverse wave is described by y = A sin(kx - omega t + phi). If the wave travels through a medium where the density