The resulting amplitude A' and the phase of the vibrationsS $$=$$ A $$cos$$$$($$ω$$t)$$ $$+$$ $$A2cos($$ω$$t+$$π$$2)+A4cos($$ω$$t+$$π$$)+A8cos($$ω$$t+3$$$$π$$$$2)$$ $$=$$ A'$$cos$$$$($$ω$$t+$$δ$$)then$$ A' and δ are respectively.

Correct option is 2358A, tan-1(12)

Questions

The resulting amplitude A' and the phase of the vibrations
S = $A \cos (ωt) + \frac{A}{2} \cos (ωt + \frac{π}{2}) + \frac{A}{4} \cos (ωt + π) + \frac{A}{8} \cos (ωt + \frac{3 π}{2}) = A^{'} \cos (ωt + δ)$
then A' and $δ$ are respectively.

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58A, tan-1(12)

358A, tan-1(12)

358A, tan-1(14)

38A, tan-1(14)

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detailed solution

Correct option is B

tan θ = 12Anet = (3A4)2+(3A8)2 = 3A41+(12)2 = 358A

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The resulting amplitude A' and the phase of the vibrationsS = A cos(ωt) + A2cos(ωt+π2)+A4cos(ωt+π)+A8cos(ωt+3π2) = A'cos(ωt+δ)then A' and δ are respectively.

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Ready to Test Your Skills?

free study material

The resulting amplitude A' and the phase of the vibrations
S = $A \cos (ωt) + \frac{A}{2} \cos (ωt + \frac{π}{2}) + \frac{A}{4} \cos (ωt + π) + \frac{A}{8} \cos (ωt + \frac{3 π}{2}) = A^{'} \cos (ωt + δ)$
then A' and $δ$ are respectively.