Question

Assertion : The amplitude of oscillation can never be infinite.
Reason : The energy of oscillator is continuously dissipated.

• A. If both assertion and reason are true and reason is the correct explanation of assertion.
• B. If both assertion and reason are true and reason is not the correct explanation of assertion.
• C. If assertion is true but reason is false.
• D. If both assertion and reason are false.

Answer 1

The correct option is A If both assertion and reason are true and reason is the correct explanation of assertion.

$A=\frac{F_0/m}{\sqrt{({\omega }^2-{\omega }_0^2{)}^2+(b\omega /m{)}^2}}$
From the above equation, the amplitude of oscillation, in absence of damping force(b = 0), that the steady-state amplitude approached infinity as $\omega \to {\omega }_0$. That is, if there is no resistive force in the system and then it is possible to drive an oscillator with sinusoidal force at the resonance frequency, the amplitude of motion will build up without limit. This does not occur in practice because some damping is always present in real oscillation. Due to the presence of various dissipative forces in the system, the amplitude of oscillation can grow to a large value only but can never be infinite.
The graph showing amplitude as a function of frequency for the forced oscillator with varying resistive force.