A) a
B) \[2a\]
C) \[\sqrt{2}a\]
D) \[\frac{a}{\sqrt{2}}\]
Correct Answer: C
Solution :
Given, \[{{y}_{1}}=a\sin \omega t\] and \[{{y}_{2}}=a\cos \omega t\] \[\Rightarrow \] \[{{y}_{2}}=a\sin \left( \frac{\pi }{2}-\omega t \right)\] ?(ii) From Eqs. (i) and (ii), we get \[{{a}_{1}}=a,\,{{a}_{2}}=a,o|=\frac{\pi }{2}\] Hence, resultant amplitude \[R=\sqrt{a_{1}^{2}+a_{2}^{2}+2{{a}_{1}}{{a}_{2}}\cos \text{o }\!\!|\!\!\text{ }}\] \[=\sqrt{{{a}^{2}}+{{a}^{2}}+2{{a}^{2}}\cos \frac{\pi }{2}}\] \[=\sqrt{{{a}^{2}}+{{a}^{2}}}=\sqrt{2}\,a\]You need to login to perform this action.
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