Question

Find the resultant amplitude of the following simple harmonic equations:

$x_{1}=5sin \, ωt$

$x_{2}=5sin\left(ωt + 53 ^\circ \right)$

$x_{3}=-10cosωt$

• A. $5$
• B. $10$
• C. $15$
• D. $20$

Answer 1

Answer: (B)

$x_{1}=5sin \, ωt$
$x_{2}=5sin\left(ωt + 53 ^\circ \right)$
$x_{3}=-10cosωt$
we can write $x_{3}=10sin\left(ωt - 90 ^\circ \right)$ Finding the resultant amplitude by vector notation.

Resultant Amplitude $\left|\right.R\left|\right.=\sqrt{8^{2} + 6^{2}}=10$ .