Discussion
Forcing the oscillator \( y'' + y \) with \( \sin 2x \) produces the particular integral
Answer: C
For a sine of angular frequency two, the operator \( d^{2}/dx^{2} \) replaces \( \sin 2x \) by \( -4\sin 2x \):
\[ \left(-4 + 1\right)A\sin 2x \;=\; \sin 2x \quad \Longrightarrow \quad A \;=\; -\tfrac{1}{3}. \]
The negative sign is essential and follows from \( -4 + 1 = -3 \). Resonance, which would bring in a factor of \( x \), happens only if the forcing frequency equals one
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development