AmTran_Bus
  • AmTran_Bus
Show c1 sin omega t + c2 cos omega t is equal to A sin (omega t + phi)
Mathematics
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AmTran_Bus
  • AmTran_Bus
Show c1 sin omega t + c2 cos omega t is equal to A sin (omega t + phi)
Mathematics
jamiebookeater
  • jamiebookeater
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AmTran_Bus
  • AmTran_Bus
|dw:1442673851220:dw| The issue is that I do not understand what omega or phi is.
ParthKohli
  • ParthKohli
Did you try to compare both equations?
ParthKohli
  • ParthKohli
\[A\sin(\omega t + \phi) \]\[= c_1 \sin (\omega t) + c_2 \cos(\omega t)\]\[= \color{#c00}{A\cos (\phi)} \sin (\omega t) + \color{#C00}{A \sin (\phi)} \cos(\omega t) \]

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anonymous
  • anonymous
Basically \[\omega,\phi,A\] These 3 quantities are constant while t is variable, so as @ParthKohli has highlighted, the quantity Acos(phi) and Asin(phi) may be clubbed together as a single constant like \[C_{1}=A\cos(\phi) \space \space \space ,\space \space \space C_{2}=A\sin(\phi)\]

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