Calculating Amplitude and Phase for Superimposed Harmonic Oscillators

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SUMMARY

The discussion focuses on calculating the resultant amplitude and phase of two superimposed harmonic oscillators with amplitudes of 5 mm and 3 mm, and a phase difference of 30°. To find the resultant amplitude, one must apply the principle of superposition and use trigonometric identities. The mathematical expressions for each wave as a function of angular frequency (wt) are essential for deriving the final amplitude and phase. Graphing the oscillators manually is recommended for visual understanding.

PREREQUISITES
  • Understanding of simple harmonic motion
  • Knowledge of trigonometric identities
  • Familiarity with phase angles in oscillatory systems
  • Ability to graph functions on Cartesian coordinates
NEXT STEPS
  • Study the principle of superposition in wave mechanics
  • Learn how to derive resultant amplitude using trigonometric methods
  • Explore the concept of phase difference in oscillatory systems
  • Practice graphing harmonic oscillators to visualize superposition
USEFUL FOR

Students of physics, engineers working with oscillatory systems, and anyone interested in wave mechanics and harmonic analysis.

kidia
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Can anybody give me the hint where to start on this question?

Two simple harmonic oscillators of the same frequency and in the same direction having amplitudes 5 mm and 3 mm, respectively and the phase of the second component relative to the first is 30°, are superimposed. Find the amplitude of the resultant oscillation and its phase relative to the first component.
 
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Whether or not it will suffice as "properly done," try manually graphing these waves on graph paper (two cycles of each wave, max), and adding their amplitudes to find the superimposed amplitude. It will give you insight to what is going on.

If you need to show the math, begin by finding the expression for amplitude for each wave as a funtion of wt.
 

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