What is Coupled oscillations: Definition and 13 Discussions
Oscillation is the repetitive variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. The term vibration is precisely used to describe mechanical oscillation. Familiar examples of oscillation include a swinging pendulum and alternating current.
Oscillations occur not only in mechanical systems but also in dynamic systems in virtually every area of science: for example the beating of the human heart (for circulation), business cycles in economics, predator–prey population cycles in ecology, geothermal geysers in geology, vibration of strings in guitar and other string instruments, periodic firing of nerve cells in the brain, and the periodic swelling of Cepheid variable stars in astronomy.
Same instruction was given while finding value of 'g' by a bar pendulum.
In the former case,does the spring obeys hooke's law while it forms a coupled harmonic oscillator system?Does the bar pendulum somehow breaks the simple harmonic motion(such that we can't apply the law for sumple harmonic...
Starting with a), I have learnt that the potential energy function has a minimum at the equilibrium distance ##a##. So at the equilibrium distance the derivative of the potential energy function should equal zero:
##\begin{align}
V'(a)&=-\frac{4A}{a^5}+\frac{B}{a^2}=0 \nonumber \\
\iff...
Suppose I have some observables \alpha, \beta, \gamma whose central values and uncertainties \sigma_{\alpha}, \sigma_{\beta}, \sigma_{\gamma} are known.
Define a function f(\alpha, \beta, \gamma) which has both real and complex parts. How do I do standard error propagation when imaginary...
I have done an experiment changing the mass ratio of coupled pendulums. To conclude I need real world applications for the coupled pendulums. But, i cannot find it online. So, it would be really helpful is someone could give examples of this. THANKS!
I would like to know how to solve the coupled pendulums problem when the masses of the pendulums are different. BUT the ratio of the masses are known and all other factors are kept constant. Need to find its affect on the beating frequency, but i cannot an equation for this with different...
Homework Statement
Two harmonic oscillators A and B , of mass m and spring constants kA and kB are coupled together by a spring of spring constant kC .Find the normal frequencies ω' and ω'' and describe the normal modes of oscillation if (k C)2= kAkB)
Homework EquationsThe Attempt at a...
So, my question is what does the "normal" part mean when one talks about normal frequencies and normal modes in coupled oscillations. Does it have to do with the normal coordinates that one uses when solving some problems, or with normal in the sense of orthogonal. Thanks for your help.
Hi there! First Post :D
In a recent CM module we've been looking at coupled oscillators and the role of time translational invariance in the description of such physical systems. I will present the statement that I am having trouble understanding and then continue to elaborate.
In stating that...
Homework Statement
An object A with mass 3m is suspended from a fixed point O by a spring of constant k. A second object B with mass 2m is in turn suspended from A by an identical spring. The system moves along a vertical axis through O. Find the frequencies of the normal modes, and the...
I have a burning question,
I was trying to find the solutions for a double mass coupled oscillation. So I found out the eigenvectors and then I arrived at this step
\left( \begin{array}{c} \ddot{x_1} \\ \ddot{x_2} \end{array} \right)=\lambda \left( \begin{array}{c} x_1 \\ \ x_2 \end{array}...
I have a system that consist of the first spring attached to a ceiling and a first mass is attached to this spring. Then a second spring is attached to this first mass. Finally I have another mass attached to the second spring. So all of it is just hanging down. (I hope this is a good enough...