Question

Why does amplitude increase at resonance?

Answer 1

Hint: In order to solve this question, we should know about the standard definition of amplitude and resonance. When a body vibrates with some natural frequency and it forces to vibrate another system to vibrate at higher amplitude is known as resonance whereas the amplitude is the maximum displacement of a vibrating body it makes from mean position to its Ext reposition along the oath of vibration.

Complete answer:
Let us suppose a body is vibrating with its amplitude and natural frequency and when a periodic external force is applied on it with the frequency equal to the natural frequency of body, then it will increase the amount of total energy on the body which in result increase in the amplitude of the body, and this whole phenomenon is known as resonance.

This external force reduces the damping of the resonating body and lessens the damping higher the amplitude of the body, while resonator bodies have increased amplitudes. There is a dimensionless parameter known as Quality factor denoted as Q-factor which is the ratio of initial energy stored in resonators to the energy consumed in past one cycle and the Q-factor is widely used to study the nature of resonating bodies.
$Q\,factor = \dfrac{{Energ{y_{stored}}}}{{{E_{dissipated}}}}$
Higher the Quality factor of a resonator higher the resonance frequency and thus the body will resonate at higher amplitudes.

Note: It should be noted that damping means when a body resonates and due to various forces like air friction or medium friction it loses its energy and thus the amplitude of the resonating body decreases. This is known as Damping of a resonating body.