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Now the real problem I'm having is trying to decide what the forces are acting on the system in order to come up with my differential equation? As there are no external forces the linear momentum of the system will be constant of motion and the constant can be taken as zero as well. If m1 and m2 are the masses at any time described by position ...


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To do the equations of motion you need positions from an inertial reference frame. Say a wall far away. Call positions of the two masses $x_1$ and $x_2$. The spring force (tension is positive) is $$ F = k (x_2-x_1 ) $$ and the two equations of motion $$\begin{align} F & = m_1 \ddot{x}_1 \\ -F & = m_2 \ddot{x}_2 \end{align} $$ All this is trivial. ...


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Assuming the spring is "ideal" (massless) you actually have 2 masses. You can describe your problem as the motion of the center of mass, and either of the masses. And if no external force is exerted on your system, you are only left with the motion of 1 mass relative to the center of the mass of the system. Let's say your masses are m1, m2, and the spring ...


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The paper by Yusuf Billah and Robert Scanlan (cited in the wikipedia article on the Tacoma Narrows Bridge 1940) distinguishes between resonance as a response to a driving force and what the authors call "self-excitation" or "negative damping." They demonstrate that the Karman Vortex Street (which occurs at the trailing edge of the deck) was not the cause of ...


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When working with waves the wavelength and frequency (pitch) are inversely related. Sound waves have the relation frequency times wavelength equal the speed of sound. Wind instruments are using the longitudinal dimension of air in the instrument as a medium like a "string". In both the string and wind instruments, shorter wavelengths in the excited medium ...


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Wind instruments work by setting up sanding waves in the air column inside them. Shorter instruments have shorter air columns and thus standing waves with shorter wavelengths resulting in higher pitches.


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The discussion which has ensued from the question here and in A conceptual doubt regarding forced oscillations and resonance hinges on how resonance is defined for particular situations and what is meant by the natural frequency of the driven system. An often used definition of resonance is: Resonance is the maximum steady state response of a driven ...


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This is known as Helmholtz resonance. Essentially, the volume of air in the cavity acts as a spring where the spring constant is dependent on the volume of the air, and damping is dependent on the inertia of air in the neck of the bottle or container. The frequency is: or: frequency = speed of sound / 2 pi * sqrt (opening area / cavity volume * length ...


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I'm assuming that you are asking this question in context of an L-C circuit. The reasonant frequency of an L-C circuit is given by the formula $$f = \frac{1}{2\pi}\sqrt{\frac{L}{C}}$$ where L is the inductance of the inductor and C is the capacitance of the capacitor. Hence if any of these two values are changed the reasonant frequency of the circuit will ...



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