Distance travelled by a particle in text{SHM} | vedclass

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(D) The displacement of a particle in $	ext{SHM}$ is given by $x = A \sin(\phi)$,where $A$ is the amplitude and $\phi$ is the phase.For the initial p

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$A$

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(D) The displacement of a particle in $	ext{SHM}$ is given by $x = A \sin(\phi)$,where $A$ is the amplitude and $\phi$ is the phase.For the initial phase $\phi_1 = \frac{\pi}{6}$,the position is $x_1 = A \sin(\frac{\pi}{6}) = A 	imes \frac{1}{2} = \frac{A}{2}$.For the final phase $\phi_2 = \frac{5\pi}{6}$,the position is $x_2 = A \sin(\frac{5\pi}{6}) = A \sin(\pi - \frac{\pi}{6}) = A \sin(\frac{\pi}{6}) = A 	imes \frac{1}{2} = \frac{A}{2}$.Since the particle moves from $x_1 = \frac{A}{2}$ to the extreme position $x = A$ and then back to $x_2 = \frac{A}{2}$,the distance travelled is the sum of the distances covered in these two parts.Distance = $(A - \frac{A}{2}) + (A - \frac{A}{2}) = \frac{A}{2} + \frac{A}{2} = A$.

Distance travelled by a particle in $\text{SHM}$ when its phase changes from $\frac{\pi}{6}$ to $\frac{5 \pi}{6}$ is:

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