If an object on a horizontal, frictionless surface is attached to a spring, displaced, and then released, it will oscillate. If it is displaced 0.120 m from its equilibrium position and released with zero initial speed, then after 0.800 s its displacement is found to be 0.120 m on the opposite side, and it has passed the equilibrium position once during this interval. Find (a) the amplitude; (b) the period; (c) the frequency.
Solution 2E The maximum displacement from a mean position of an object is known as the amplitude. (a) In the question, it is given that the spring is displaced to 0.120 m from equilibrium position, Therefore, this is the amplitude of the given oscillation. Time period is defined as the time required to complete one complete oscillation. (b) In the given question, the spring moves 0.120 m from the maximum displacement position in 0.800 s. Since the surface is frictionless, the spring will moves back to the same position from where it was released. Therefore, it would take the same time to reach this distance. Hence total time taken to complete one oscillation is = 0.800 + .800 s = 1.600 s. So, the period is 1.600 s. (c) Since one oscillation takes place in 1.600 s, hence the frequency of oscillations is, f = 1/period = 1/1.600 Hz = 0.625 Hz