To solve this problem, we need to find the expression for acceleration $a$ in terms of time $t. \\$Given the displacement equation:$\\ x = A \cos(\omega t) \\$The velocity $v$ is the derivative of displacement with respect to time:$\\ v = \frac{dx}{dt} = -A \omega \sin(\omega t) \\$The acceleration $a$ is the derivative of velocity with respect to time:$\\ a = \frac{dv}{dt} = -A \omega^2 \cos(\omega t) \\$This shows that acceleration is proportional to $\cos(\omega t),$ which is the same as the displacement equation.$\\$The graph of acceleration versus time will be a cosine wave, similar to the displacement graph.$\\$Let's analyze the options:$\\$• Option 1: Shows a sine wave, not correct.$\\$• Option 2: Shows a half sine wave, not correct.$\\$• Option 3: Shows a cosine wave, which matches $a = -A \omega^2 \cos(\omega t). \\$• Option 4: Shows a shifted sine wave, not correct.$\\$Therefore, the correct graph is Option 3, which correctly represents the variation of acceleration with time.