Two simple harmonic motions along the same axis are given by x_1 = 3sin(omegat) and x_2 = 4cos(omegat). What is the amplitude of the resultant motion?
Answer and explanation
Correct answer: B. 5, combining the two orthogonal phasor components via Pythagoras theorem
- Step 1: Since cos(omegat) = sin(omegat + pi/2), the two oscillations have a 90-degree phase difference. Step 2. Using phasor addition: A_res = sqrt(A_1^2 + A_2^2) = sqrt(3^2 + 4^2) = sqrt(9 + 16) = 5. Answer: 5, combining the two orthogonal phasor components via Pythagoras theorem. Why not the others: Linear addition only applies when the two oscillations are exactly in phase.
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