The phase difference between displacement and acceleration of a...

Displacement $( x )$ equation of SHM

$x = Asin ( \omegat + ϕ )$ ....(1)

$\dfrac{dx}{dt} = A\omega cos\left(\omegat + ϕ\right)</p><p>acceleration$\left(a\right) = \dfrac{{d}^{2}x}{d{t}^{2}}$</p><p>$a = - {\omega}^{2}Asin\left(\omegat + ϕ\right)

$a = {\omega}^{2}Asin \left(\omegat + ϕ + \pi\right)$ ....(2)

from (1) & (2), phase difference between displacement and acceleration is $\pi .</p>$