Question

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: Every solution $\phi$ of the differential equation $y'' + \omega^2 y = A \cos \omega x$; $A$ and $\omega$ are positive constants, satisfies $|\phi(x)| \to \infty$ as $x \to \infty$.
Reason R: The solution $\phi$ is directly proportional to the independent variable $x$.

• A. Both A and R are true and R is the correct explanation of A
• B. Both A and R are true but R is NOT the correct explanation of A
• C. A is true but R is false
• D. A is false but R is true

Hint:

When forcing frequency equals natural frequency ($\omega$), the particular integral contains an explicit factor of $x$, i.e., $x \sin(\omega x)$, which causes linear growth in amplitude (resonance).

Answer 1

The Correct Option is D