• # question_answer Two simple harmonic motion ${{x}_{1}}=a\sin \,\omega t$ and ${{x}_{2}}=b\cos \,\omega t$ are superimposed on a particle. The displacements ${{x}_{1}}$ and ${{x}_{2}}$ are along the same directions. Then choose the correct option. A) The particle will not perform SHM. B) The motion will not be oscillatory. C) The particle will perform SHM. D) The particle will perform periodic motion but not SHM.

[c] ${{x}_{1}}=a\sin \omega t$ and ${{x}_{2}}=b\sin \left( \omega t+\frac{\pi }{2} \right)$ From superposition principle, resultant displacement must be SHM.