The phase difference between displacement and acceleration of a particle in a simple harmonic motion is:

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1.  **Displacement Equation:** Let the displacement of a particle executing Simple Harmonic Motion (SHM) be given by:
    $$ x = A \sin(\omega t) $$
    where $A$ is the amplitude and $\omega$ is the angular frequency.
2.  **Velocity Equation:** Velocity $v$ is the time derivative of displacement:
    $$ v = \frac{dx}{dt} = A\omega \cos(\omega t) = A\omega \sin(\omega t + \frac{\pi}{2}) $$
    (Phase difference between displacement and velocity is $\pi/2$).
3.  **Acceleration Equation:** Acceleration $a$ is the time derivative of velocity:
    $$ a = \frac{dv}{dt} = \frac{d}{dt}[A\omega \cos(\omega t)] = -A\omega^2 \sin(\omega t) $$
    Using the trigonometric identity $-\sin 	heta = \sin(	heta + \pi)$, we can write:
    $$ a = A\omega^2 \sin(\omega t + \pi) $$
4.  **Phase Difference:** Comparing the phase of displacement $(\omega t)$ and acceleration $(\omega t + \pi)$, the difference is:
    $$ \Delta \phi = (\omega t + \pi) - (\omega t) = \pi 	ext{ rad} $$
5.  **Conclusion:** The acceleration is always in opposite phase ($180^\circ$ or $\pi$ radians) to the displacement .

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