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(D) In simple harmonic motion $(SHM)$,the displacement $d$ as a function of time $t$ is given by $d = A \sin(\omega t + \phi)$.To find the relationshi

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$IV$

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(D) In simple harmonic motion $(SHM)$,the displacement $d$ as a function of time $t$ is given by $d = A \sin(\omega t + \phi)$.To find the relationship where $y$ is time $(t)$ and $d$ is displacement,we rearrange the equation: $t = \frac{1}{\omega} \arcsin(\frac{d}{A}) - \frac{\phi}{\omega}$.This equation implies that for a single value of displacement $d$,there are multiple values of time $t$ as the particle oscillates back and forth.Graph $IV$ shows a relationship where for a given displacement $d$ (within the range $-A$ to $+A$),there are multiple values of $y$ (time),which correctly represents the periodic nature of $SHM$ when time is plotted on the vertical axis.

The graphs in the figure show that a quantity $y$ varies with displacement $d$ in a system undergoing simple harmonic motion. Which graph best represents the relationship obtained when $y$ is the time?

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