phase difference

Question

Two SHM motions x1 = A sin(ωt) and x2 = A cos(ωt) have phase difference?

RankGuru · Accepted Answer

1. **Standard Form**: To compare phases, functions should be in the same form (either both sine or both cosine).
2. **Trigonometric conversion**: $\cos(\omega t) = \sin(\omega t + \frac{\pi}{2})$.
3. **Identify Phases**:
   - Phase of $x_1$: $\phi_1 = \omega t$
   - Phase of $x_2$: $\phi_2 = \omega t + \pi/2$
4. **Phase Difference ($\Delta \phi$)**: $\Delta \phi = \phi_2 - \phi_1 = \frac{\pi}{2}$.
5. **Conclusion**: The cosine wave 'leads' the sine wave by **$\pi/2$** radians or $90^\circ$.

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phase difference

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