mass-spring period

Question

Period of mass m on spring constant k?

RankGuru · Accepted Answer

1. **Angular Frequency ($\omega$)**: For a spring-mass system, $\omega = \sqrt{\frac{k}{m}}$.
2. **Relating to Period (T)**: Period is the time taken for one full cycle: $T = \frac{2\pi}{\omega}$.
3. **Calculation**: 
   - $T = 2\pi \div \sqrt{\frac{k}{m}}$
   - $T = 2\pi \sqrt{\frac{m}{k}}$.
4. **Dependence**: Increasing mass slows down the oscillation (longer $T$), while a stiffer spring (higher $k$) speeds it up (shorter $T$).

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mass-spring period

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