Exercise
https://texercises.com/exercise/resonance-for-mechanical-oscillator/
Question
Solution
Short
Video
\(\LaTeX\)
No explanation / solution video to this exercise has yet been created.

Visit our YouTube-Channel to see solutions to other exercises.
Don't forget to subscribe to our channel, like the videos and leave comments!
Exercise:
The differential s for a driven series LC oscillator with damping and a driven mass on a spring with linear drag are formally equivalent: ddotqt + omega_e^ qt+ delta_e dotqt Q_cosomega t ddotyt + omega_m^ yt+ delta_m dotyt A_cosomega t with the angular frequencies for the undamped system omega_e fracsqrtLC labelome quad textrmand quad omega_m sqrtfrackm and the damping constant delta_e fracRL labeldee quad textrmand quad delta_m fracbetam Using the analogy between mechanical and electrical quantities derive the expressions for the resonance frequency of the mechanical oscillator. Calculate the numerical value for a mass mO an elastic constant kO and a drag coefficient beO.

Solution:
The displacement yt of the mass corresponds to the charge qt on the capacitor which is proportional to the capacitor voltage v_Ct. We know that the amplitude of the capacitor voltage has a maximum for omega_R sqrtomega_^-delta^ For the mechanical system we find omega_R omRF sqrtfrackm-fracbe^timesm^ omR approx resultomRP The angular frequency of the undamped system is omega_ omudF sqrtfrackm omud approx resultomudP
Report An Error
You are on texercises.com.
reCaptcha will only work on our main-domain \(\TeX\)ercises.com!
Meta Information
\(\LaTeX\)-Code
Exercise:
The differential s for a driven series LC oscillator with damping and a driven mass on a spring with linear drag are formally equivalent: ddotqt + omega_e^ qt+ delta_e dotqt Q_cosomega t ddotyt + omega_m^ yt+ delta_m dotyt A_cosomega t with the angular frequencies for the undamped system omega_e fracsqrtLC labelome quad textrmand quad omega_m sqrtfrackm and the damping constant delta_e fracRL labeldee quad textrmand quad delta_m fracbetam Using the analogy between mechanical and electrical quantities derive the expressions for the resonance frequency of the mechanical oscillator. Calculate the numerical value for a mass mO an elastic constant kO and a drag coefficient beO.

Solution:
The displacement yt of the mass corresponds to the charge qt on the capacitor which is proportional to the capacitor voltage v_Ct. We know that the amplitude of the capacitor voltage has a maximum for omega_R sqrtomega_^-delta^ For the mechanical system we find omega_R omRF sqrtfrackm-fracbe^timesm^ omR approx resultomRP The angular frequency of the undamped system is omega_ omudF sqrtfrackm omud approx resultomudP
Contained in these collections

Similar exercises (4)
Title Matched on
Oscillation Graphs formula
Speed Bump formula
LC Oscillator formula
Resonance in LCR Series Circuit tags

Attributes & Decorations
Branches
Forced Oscillations
Tags
damping, driven oscillation, lc oscillator, mass on spring
Difficulty
(2, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
Decoration
Content image