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Question #42634
The Question
A particle of mass is attached to a fixed support by a spring of force constant . The particle is subjected to a linear drag force , where and is the velocity of the particle. An external driving force (in Newtons, with in seconds) is applied to the particle along the direction of the spring. After a sufficiently long time, the system reaches a steady state. What is the average rate of energy dissipation by the drag force over a long time interval?
Options
- A.
272 \text{ W}
- B.
544 \text{ W}
- C.
512 \text{ W}
- D.
136 \text{ W}
Check Your Answer
Correct Answer
Step-by-Step Solution
Explanation
How the Examiner Thinks
Variable_Constraint
Develop pure symbolic logic skills by mastering algebraic constraints without relying on numerical data.
Concepts Behind This Question
Superposition of SHMs|Conservative vs Non-conservative|Integration
Why This Question Is Tricky
Common Mistakes
This question tests the principle of linear superposition in driven-damped harmonic oscillators and the non-linear nature of energy dissipation.
Students often incorrectly assume that the total average power can be calculated by finding a single 'effective' amplitude or by directly adding the driving forces and ignoring the phase lag (a misapplication of the Work-Energy theorem).
The trap exploits the fact that while displacement and velocity superimpose linearly, power depends on the square of velocity.
Because the driving frequencies are distinct, the time-averaged cross-terms of velocity vanish, meaning the total average power is strictly the sum of the average powers of the individual frequency components.
Quick Facts About This Question
Question Information
| Subject | Physics |
| Chapter | Oscillations - Class 11 Part 2 |
| Concept | Superposition of SHMs |
| Difficulty | 8 |
| Cognitive Load | 7 |
| Target Solve Time | 160 sec |
| Access | Free |