Calculus Volume 3 · free preview
Applications
Mechanical vibrations and RLC circuits follow the same second-order equation, the spring-mass-damper and the resistor-inductor-capacitor sharing the mathematical form, the damping's three regimes the system's behavior.
1. The spring-mass-damper
The spring-mass-damper
2. The RLC circuit
The RLC circuit
3. The regimes' interpretation
The regimes' interpretation
4. The nonlinear frontier
The nonlinear frontier
5. Spring equation terms
In the spring-mass-damper equation m x double prime plus c x prime plus k x equals F, the c x prime term models which force?
6. RLC analogy mass
In the RLC circuit's equation, the inductance L plays which mechanical role?
7. Critical damping design
A door closer or a car suspension aims for which damping regime?
8. Radio tuning
A radio selects a station by which resonance's use?
9. Quality factor
The sharpness of a resonant circuit's peak is measured by which two-letter quantity?
10. Damping coefficient letter
The damping coefficient in the spring equation is which letter? Answer with one lowercase letter.
11. Natural frequency formula
The natural frequency is the root of k over m. As a fraction, what is under the root? Answer like k/m.
12. Capacitor role
In the RLC analogy, the capacitor plays which mechanical role? Answer with one word.
13. Analogies unity
The mechanical and electrical systems share one equation because of which deeper fact?
14. Washboard road resonance
A washboard road at the right speed can resonate a car's suspension. As a two-word phrase, what is this? Answer like answer key.
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