Neet Solved Paper 2015 Question 23
Question: When two displacements represented by $ y _1=a\sin (\omega t) $ and $ y _2=b\cos ,(\omega t) $ are superimposed, the motion is
Options:
A) not a simple harmonic
B) simple harmonic with amplitude $ \frac{a}{b} $
C) simple harmonic with amplitude $ \sqrt{a^{2}+b^{2}} $
D) simple harmonic with amplitude $ \frac{(a+b)}{2} $
Show Answer
Answer:
Correct Answer: C
Solution:
Given, $ y _1=a\sin \omega t $ $ y _2=b,\cos \omega t=b\sin ( \omega t+\frac{\pi }{2} ) $
The resultant displacement is given by $ y=y _1+y _2=\sqrt{a^{2}+b^{2}}\sin (\omega t+\phi ) $
Hence, the motion of superimposed wave is simple harmonic with amplitude $ \sqrt{a^{2}+b^{2}}. $
