Physics - SHM Question with Solution | TestHub

Resultant amplitude of $x_1$ and $x_2$ is $A$ at angle $\left(\frac{\pi }{3}\right)$ from $A_1$. To make resultant of $x_1,x_2$ and $x_3$ to be zero. $A_3$ should be equal to $A$ at angle $\varphi =\frac{4\pi }{3}$ as shown in figure. $\therefore$ Correct answer is (b). Alternate Solution If we substitute, $$x_1+x_2+x_3=0$$ or $A\sin \omega t+A\sin \left(\omega t+\frac{2\pi }{3}\right)$ $$+B\sin (\omega t+\varphi )=0$$ Then, by applying simple mathematics, we can prove that $$\begin{array}{rlr}B& =A& \\ \text{ and }& \varphi & =\frac{4\pi }{3}\end{array}$$ Analysis of Question (i) Question is simple. (ii) Question can be solved by applying mathematics also. (iii) Amplitudes of two or more sine or cosine functions of same frequency $\omega$ can be added by vector method.