University of Central Florida (UCF) PSC1121 Physical Science Final Practice Exam

To find the oscillation period from the time it takes to move from the equilibrium position to the maximum extension, it's important to understand the behavior of simple harmonic motion. During one complete oscillation, an object first moves from the equilibrium position to the maximum positive displacement (maximum extension), then back to the equilibrium position, moves to the maximum negative displacement (maximum compression), and finally returns to the equilibrium position again.

The time taken to move from equilibrium to maximum extension is just a quarter of the full oscillation cycle. If it takes 0.45 seconds to reach maximum extension, then the total time for a full cycle — or the oscillation period — is four times that duration. Therefore, you multiply the 0.45 seconds by 4, resulting in an oscillation period of 1.80 seconds.

This reasoning aligns with the nature of oscillatory motion, where each phase of the cycle (equilibrium to maximum extension, maximum extension to equilibrium, equilibrium to maximum compression, and maximum compression back to equilibrium) represents equal time intervals.