Physics · Simple harmonic motion (S.H.M.) and its equation, phase
The motion of a particle is given by The motion of the particle is:
The motion of a particle is given by \( \boldsymbol{x}= \) \( a \sin \omega t+b \cos \omega t . \) The motion of the particle is:
- A. Not simple harmonic
- B. Simple harmonic with amplitude \( (A-B) / 2 \)
- C. Simple harmonic with amplitude \( (A+B) / 2 \)
- D. Simple harmonic with amplitude \( \sqrt{A^{2}+B^{2}} \)
Step-by-step solution
The expression x = a sin ωt + b cos ωt can be rewritten as R sin(ωt + φ) where R = √(a² + b²). This represents simple harmonic motion with amplitude √(a² + b²). The options use A and B instead of a and b, so the amplitude is √(A² + B²).
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