Mechanic Oscillations
Tags: #physics #mechanic #oscillationsEquation
$$m\ddot{x}=F(t)-k\dot{x}-Cx \\ F(t)=\hat{F}\cos(\omega t) \\ -m\omega^2 x=F-Cx-ik\omega x \\ \omega_0^2=C/m \\ x=\frac{F}{m(\omega_0^2-\omega^2)+ik\omega} \\ \dot{x}=\frac{F}{i\sqrt{Cm}\delta+k} \\ \delta=\frac{\omega}{\omega_0}-\frac{\omega_0}{\omega} \\ Z=F/\dot{x} \\ Q=\frac{\sqrt{Cm}}{k}$$Latex Code
m\ddot{x}=F(t)-k\dot{x}-Cx \\
F(t)=\hat{F}\cos(\omega t) \\
-m\omega^2 x=F-Cx-ik\omega x \\
\omega_0^2=C/m \\
x=\frac{F}{m(\omega_0^2-\omega^2)+ik\omega} \\
\dot{x}=\frac{F}{i\sqrt{Cm}\delta+k} \\
\delta=\frac{\omega}{\omega_0}-\frac{\omega_0}{\omega} \\
Z=F/\dot{x} \\
Q=\frac{\sqrt{Cm}}{k}
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Introduction
Equation
Latex Code
m\ddot{x}=F(t)-k\dot{x}-Cx \\
F(t)=\hat{F}\cos(\omega t) \\
-m\omega^2 x=F-Cx-ik\omega x \\
\omega_0^2=C/m \\
x=\frac{F}{m(\omega_0^2-\omega^2)+ik\omega} \\
\dot{x}=\frac{F}{i\sqrt{Cm}\delta+k} \\
\delta=\frac{\omega}{\omega_0}-\frac{\omega_0}{\omega} \\
Z=F/\dot{x} \\
Q=\frac{\sqrt{Cm}}{k}
Explanation
Latex code for the Mechanic Oscillations. I will briefly introduce the notations in this formulation.
: Construction of spring with constant
: Damping constant
: Periodic force
: Velocity
: Impedance of the system
: The quality of the system
- Velocity resonance frequency: The frequency with minimal
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The tension is high, but I'm hopeful I'll pass this exam.
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