A floating scientific buoy performs vertical oscillations in calm water, behaving as a simple harmonic oscillator. The buoy is depressed vertically and released from rest at time t=0t = 0t=0. It oscillates freely with negligible damping.
At time t=2.4 st = 2.4\text{ s}t=2.4 s, the magnitude of the displacement y y\,y of the buoy from its equilibrium position is 0.12 m, and the magnitude of its acceleration a a\,a is 1.08 m s-2.
Use the defining equation for simple harmonic motion to show that the natural frequency f0 f_0\,f0 of the buoy's vertical oscillations is approximately 0.48 Hz.
Calculate the amplitude A A\,A of the oscillations.
