A) SHM with amplitude \[\sqrt{{{A}^{2}}+{{B}^{2}}}\]
B) SHM with amplitude \[A+B\]
C) SHM with amplitude\[A\]
D) Oscillatory but not in SHM
Correct Answer: A
Solution :
\[y=A\sin \omega t+B\cos \omega t\] ?(1) let \[A=a\cos \phi \] ?(2) \[B=a\cos \phi \] ?(3) then equation (1) becomes \[y=a\cos \phi \sin \omega t+a\sin \phi \cos \omega t\] \[y=a\sin \,(\omega t+\phi )\] ?(4) It is clear that the equation number (2) in simple harmonic motion with amplitude a squaring and adding (2) and (3), we get \[{{A}^{2}}+{{B}^{2}}\le {{a}^{2}}(co{{s}^{2}}\phi +si{{n}^{2}}\phi )\] \[a=\sqrt{{{A}^{2}}+{{B}^{2}}}\]
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