The maximum speed of the mass is given by the formula:
\[v_{\text{max}} = \omega\cdot A\]
where \(\omega\) is the angular frequency and \(A\) is the amplitude.

The angular frequency can be calculated using the formula:
\[\omega = \frac{2\pi}{T}\]
where \(\omega\) is the angular frequency and \(T\) is the period.

Given that the period \(T\) is 2 seconds, we can substitute this value into the formula to get:
\[\omega = \frac{2\pi}{2} = \pi \,\text{rad/s}\]

Given that the amplitude \(A\) is 0.5 meters, we can substitute this value into the formula to get:
\[v_{\text{max}} = \pi \cdot 0.5 = \frac{\pi}{2} \approx 1.57 \,\text{m/s}\]

Thus, the maximum speed of the mass is approximately \(1.57 \,\text{m/s}\).

The acceleration of the mass at maximum displacement can be calculated using the formula:
\[a_{\text{max}} = \omega^2 \cdot A\]
where \(a_{\text{max}}\) is the acceleration and \(\omega\) is the angular frequency.

Using the given values of \(\omega = \pi \,\text{rad/s}\) and \(A = 0.5 \,\text{meters}\), we can substitute these values into the formula to get:
\[a_{\text{max}} = (\pi)^2 \cdot 0.5 = \pi^2 \cdot 0.5 \approx 4.93 \,\text{m/s}^2\]

Thus, the acceleration of the mass at its maximum displacement is approximately \(4.93 \,\text{m/s}^2\).

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