A machine is subjected to the vibration

\[x(t)=20 \sin 50 t+5 \sin 150 t \mathrm{~mm} \quad(t \text { in } \mathrm{s})\]

An accelerometer having a damped natural frequency of \(80 \mathrm{rad} / \mathrm{s}\) and an undamped natural frequency of \(100 \mathrm{rad} / \mathrm{s}\) is mounted on the machine to read the acceleration directly in \(\mathrm{mm} / \mathrm{s}^{2}\). Discuss the accuracy of the recorded acceleration.