Comparison of Euler and Euler-Cromer Numerical Methods for Undamped and Damped Spring Oscillation
DOI:
https://doi.org/10.12928/irip.v4i2.4803Keywords:
Damped Oscillation, Undamped Oscillation, Euler Method, Euler-Cromer MethodAbstract
This study aimed to numerically analyze damped and undamped oscillations of a spring using the Euler and Euler-Cromer methods via Spreadsheet software. The varied parameters in this study were the damping constant, namely 0.1 (damped) and 0.0 (undamped). Various quantities analyzed in this study were position (x), velocity (v), kinetic energy (K), potential energy (U), mechanical energy (E), and phase space as a function of time (t). Iteration was done in t < 60-time steps (seconds). The results of this study indicated that when the spring experiences damping, the numerical results of x, v, K, U, E, and the phase space decrease periodically to zero due to the damping force, both for the Euler and Euler-Cromer methods. Meanwhile, for the undamped spring (zero damping constant), there was a difference in the results for the Euler and Euler-Cromer methods. For the Euler method, the resulting values of x, v, K, U, E, and the phase space increased periodically with time, which was not following the actual situation. According to the simple harmonic oscillation, the Euler-Cromer method values of x, v, K, U, E, and the phase space were stable over time.
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