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(B) The general equation for $SHM$ is $x = A \sin(\omega t + \phi)$,where $\omega = \frac{2\pi}{T}$.At $t = 0$,the particle is at $x = +A/2$ and movin

Vedclass · Accepted Answer

$x = A \sin \left( \frac{2\pi}{T}t + \frac{5\pi}{6} \right)$

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(B) The general equation for $SHM$ is $x = A \sin(\omega t + \phi)$,where $\omega = \frac{2\pi}{T}$.At $t = 0$,the particle is at $x = +A/2$ and moving towards the left (negative direction).Substituting $t = 0$ into the equation: $A/2 = A \sin(\phi)$,which gives $\sin(\phi) = 1/2$.This implies $\phi = \pi/6$ or $\phi = 5\pi/6$.Since the particle is moving towards the left (towards the mean position from the positive side),its velocity $v = dx/dt = A\omega \cos(\omega t + \phi)$ must be negative at $t = 0$.For $\phi = \pi/6$,$v = A\omega \cos(\pi/6) > 0$.For $\phi = 5\pi/6$,$v = A\omega \cos(5\pi/6) Thus,the correct phase constant is $\phi = 5\pi/6$.The equation of motion is $x = A \sin \left( \frac{2\pi}{T}t + \frac{5\pi}{6} \right)$.

$A$ particle starts from a point $P$ at a distance of $A/2$ from the mean position $O$ and travels towards the left as shown in the figure. If the time period of $SHM$ executed about $O$ is $T$ and amplitude is $A$,then the equation of motion of the particle is:

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