Abir Sarkar said:Under appreciable damping , Why amplitude resonance and Velocity resonance occurs at slightly different frequencies ?
- Abir Sarkar
A damped simple harmonic oscillation is a type of motion in which an object moves back and forth with a decreasing amplitude due to the presence of a damping force. This type of oscillation is commonly observed in systems such as springs, pendulums, and electrical circuits.
Damping in a simple harmonic oscillator is caused by the presence of external forces, such as friction or air resistance, that act against the motion of the object. These forces decrease the amplitude of the oscillation over time, resulting in a damped oscillation.
The damping coefficient, or the measure of the strength of the damping force, is directly related to the amplitude of a damped simple harmonic oscillator. A higher damping coefficient results in a faster decrease in amplitude, while a lower damping coefficient allows the oscillation to continue for a longer period of time.
Underdamped oscillations occur when the damping force is not strong enough to stop the oscillation, resulting in a gradual decrease in amplitude. Critically damped oscillations occur when the damping force is just enough to stop the oscillation from continuing. Overdamped oscillations occur when the damping force is too strong, causing the object to return to its equilibrium position without oscillating.
In a damped simple harmonic oscillator, the energy is not conserved due to the presence of external forces that dissipate energy. As the amplitude decreases, the kinetic energy of the object also decreases while the potential energy increases. Eventually, all of the energy is dissipated by the damping force, and the object comes to rest at its equilibrium position.