A) 1
B) 3
C) 4
D) 5
Correct Answer: B
Solution :
\[y=4{{\cos }^{2}}\frac{t}{2}.\sin 1000t\] \[=2\left( 2{{\cos }^{2}}\frac{t}{2} \right).\sin 1000t\] \[=2(1+\operatorname{cost}).\sin 1000t\] \[=2\sin 1000t+2\cos t.\sin 1000t\] \[=2\sin 1000t+\sin (1000+1)t\] \[\sin (1000t-t)\] \[=2\sin 1000t+\sin 1001t+\sin 999t\] \[[\because 2\sin A\cos B=\sin (A+B)+\sin (A-B)]\] \[={{y}_{1}}+{{y}_{2}}+{{y}_{3}}\] So, the given expression may be considered as the result of superposition of 3 independent harmonic motions.You need to login to perform this action.
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