Addendum: Modeling the amplitude and energy decay of a weakly damped harmonic oscillator using the energy dissipation rate and a simple trick (2025 Eur. J. Phys. 46(1) 015004)
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| Format: | Preprint |
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2024
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| _version_ | 1866916932592074752 |
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| author | Lelas, Karlo Pezer, Robert |
| author_facet | Lelas, Karlo Pezer, Robert |
| contents | We show how to adapt the approach introduced for viscous damping in [1] to derive the approximate amplitude decay in the case of damping by a force of constant magnitude (sliding friction) and in the case of damping by a force proportional to the square of velocity (air resistance). We obtain two first-order differential equations from which we obtain the approximate time-dependent amplitudes corresponding to the considered damping forces. Our approach is suitable for first-year undergraduates, as it relies on the physical concepts and mathematical techniques they are familiar with. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_15588 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Addendum: Modeling the amplitude and energy decay of a weakly damped harmonic oscillator using the energy dissipation rate and a simple trick (2025 Eur. J. Phys. 46(1) 015004) Lelas, Karlo Pezer, Robert Classical Physics We show how to adapt the approach introduced for viscous damping in [1] to derive the approximate amplitude decay in the case of damping by a force of constant magnitude (sliding friction) and in the case of damping by a force proportional to the square of velocity (air resistance). We obtain two first-order differential equations from which we obtain the approximate time-dependent amplitudes corresponding to the considered damping forces. Our approach is suitable for first-year undergraduates, as it relies on the physical concepts and mathematical techniques they are familiar with. |
| title | Addendum: Modeling the amplitude and energy decay of a weakly damped harmonic oscillator using the energy dissipation rate and a simple trick (2025 Eur. J. Phys. 46(1) 015004) |
| topic | Classical Physics |
| url | https://arxiv.org/abs/2411.15588 |