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UnkleRhaukus

  • one year ago

Perpendicular Simple Harmonic Oscillators A particle is simultaneously subjected to two perpendicular simple harmonic oscillators of the same frequency, 112 Hz. If the amplitude and phase constant of one oscillator is 0.64mm and 21° respectively, and the other is 0.16mm and 83°, determine the resultant amplitude at 9.8 seconds.

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  1. IrishBoy123
    • one year ago
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    |dw:1442320340503:dw|

  2. IrishBoy123
    • one year ago
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    just like a phasor?

  3. IrishBoy123
    • one year ago
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    sorry they're orthogomal let's think

  4. UnkleRhaukus
    • one year ago
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    uhm

  5. IrishBoy123
    • one year ago
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    |dw:1442320936419:dw|

  6. UnkleRhaukus
    • one year ago
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    ¿it flipped

  7. IrishBoy123
    • one year ago
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    ie, i'd be looking to use \(A_1 e^{i (\omega t + \delta_1)} + i \ A_2 e^{i (\omega t + \delta_2)} \) if i could make it work

  8. IrishBoy123
    • one year ago
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    because crunching \(\sqrt{ A_1^2 cos^2 (\omega t + \delta_1) + A_2^2 cos^2 (\omega t + \delta_2) }\) would be a pain

  9. UnkleRhaukus
    • one year ago
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    is that the amplitude

  10. UnkleRhaukus
    • one year ago
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    oh , i see it flipted because they are perpendicular!

  11. IrishBoy123
    • one year ago
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    yes but it proves the idea is totally totally hair brained i think, and mixes up 2 ideas. the flip just adds a phase shift to the second shm but is modelling them in 1 dimension i have searched the web and no one is using phasors for shm, except in 1 dimension, which makes sense i suppose. http://www.wolframalpha.com/input/?i=sqrt+%28%280.16+cos+%282+*pi+*+112+*+9.8+++%2B+83%2Fpi+%29+%29%5E2%2B+%280.64+cos+%282+*pi+*+112+*+9.8+++%2B+21%2Fpi+%29%29%5E2%29

  12. UnkleRhaukus
    • one year ago
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  13. UnkleRhaukus
    • one year ago
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    i solved it this way, with the aid of the phasor graph, i've assumed sines whereas you've got cosines,

  14. IrishBoy123
    • one year ago
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    holy moley that's interesting can't ope the attachment but i will definitely go back and study this again thx

  15. UnkleRhaukus
    • one year ago
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    i drew the ellipse

  16. UnkleRhaukus
    • one year ago
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    |dw:1442404085179:dw|

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