Test: Damped & Forced Oscillations - JEE MCQ

The phenomenon of increase in amplitude when the driving force is close to the natural frequency of the oscillator is known as resonance. By the definition of resonance.

When the natural frequency and external frequency of an object are equal the phenomenon is called resonance.

The restoring force in a simple harmonic motion is maximum in magnitude when the particle is instantaneously at rest because in SHM object’s tendency is to return to mean position and here particle is instantaneously at rest after that instant restoring force will be max to bring particle to mean position.

Energy is supplied to the damped oscillatory system at the same rate at which it is dissipating energy, and then the amplitude of such oscillations would become constant. Such oscillations are called maintained oscillations. By the definition of maintained oscillations.

In an ideal environment where there is no resistance to oscillation motion i.e. damping is zero, when we oscillate a system at its resonant frequency since there is no opposition to oscillation, the amplitude will go on increasing and reach infinity.

Natural frequency is the frequency at which a body tends to oscillate in the absence of any driving or damping force.
Free vibrations of any elastic body are called natural vibration and happen at a frequency called natural frequency. Natural vibrations are different from forced vibration which happen at frequency of applied force .

Simple when wd = w then resonance happens and in resonance amplitude is max.

Harmonic motion is the natural motion of a body(we consider no air friction) under no force where as damped oscillation are under force hence the iscilation are different

In an ideal environment where there is no resistance to oscillatory motion, that is, damping is zero, when we oscillate a system at its resonant frequency, since there is no opposition to oscillation, a very large value of amplitude will be recorded. Forced oscillation is when you apply an external oscillating force.