A horizontal test-mass within a precision seismometer calibration rig acts as a simple harmonic oscillator. The test-mass is displaced from its neutral equilibrium position and released from rest at time t=0t = 0t=0. It oscillates horizontally with negligible friction.
At time t=2.4 st = 2.4\text{ s}t=2.4 s, the magnitude of the horizontal acceleration aaa of the test-mass is 4.0 m s−24.0\text{ m s}^{-2}4.0 m s−2 and its displacement magnitude xxx is 4.5×10−2 m4.5 \times 10^{-2}\text{ m}4.5×10−2 m.
Use the defining equation for simple harmonic motion to show that the natural frequency f0f_0f0 of the calibration rig's test-mass is approximately 1.5 Hz1.5\text{ Hz}1.5 Hz.
Calculate the amplitude AAA of the oscillations.
