Directions: In the following question more than one of the answers given may be correct. Select the correct answer and mark it according to the code:
Function\[x=A{{\sin }^{2}}\omega t+B{{\cos }^{2}}\omega t\] \[+C\sin \omega t\cos \omega t\]of represents SHM: (1) for any value of A, B and C (except\[C=0\]) (2) If\[A=-B,C=2B,\]amplitude\[=|B\sqrt{2}|\] (3) If\[A=B,\text{ }C=2B,\]amplitude\[=|B|\] (4)If \[A=B,C=0\]A) 1 and 2 are correct
B) 2 and 3 are correct
C) 1 and 4 and correct
D) 1, 2 and 4 are correct
Correct Answer: B
Solution :
For\[A=-B\]and\[C=2B\] \[x=B\cos \,2\,\omega t+B\sin \,2\,\omega t\] \[=\sqrt{2}B\sin \left( 2\omega t+\frac{\pi }{4} \right)\] This is the equation of SHM of amplitude\[\sqrt{2}B\] If\[A=B\]and\[c=28,\]then \[x=B+B\text{ }sin\text{ }2\omega t\] This is also equation of SHM about the point \[x=B\]. Function oscillates between;\[c=0\]and \[x=28\]with amplitude B.
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