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rahaverhma
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Why would normal modes occur in the coupled oscillator system I.e. why the parts of system would oscillate with constant angular frequency and constant phase difference ?
If the network were to alter the frequency, it would need to change the shape of the wave whilst doing so. For example, a frequency modulated wave is not sinusoidal.rahaverhma said:Why would normal modes occur in the coupled oscillator system I.e. why the parts of system would oscillate with constant angular frequency and constant phase difference ?
Displacement is proportional to force (Hooke's Law).rahaverhma said:Actually I had come across a question of 2 springs ,2 blocks suspended by wall under gravity.And I think the shape of wave would not change because there is only vertical oscillations .Yeah,the system has linear equation ,but what do we mean by this ?
But how can I know that they both will be oscillating at same frequencies.And which u hv said that only tells about the frequency of parts of a system.I mean omega is unique for the components .tech99 said:Displacement is proportional to force (Hooke's Law).
The system would not do this unless you set up the proper initial conditions in such a way as to determine the system to oscillate in a normal mode.rahaverhma said:Why would normal modes occur in the coupled oscillator system I.e. why the parts of system would oscillate with constant angular frequency and constant phase difference ?
Normal modes in a coupled system refer to the natural oscillations or vibrations of the system when it is disturbed from its equilibrium position. These modes are characterized by specific frequencies and amplitudes, and are independent of the initial conditions.
Normal modes can be calculated using mathematical methods such as eigenvalue analysis, where the system's equations of motion are solved for the eigenvalues and eigenvectors. These eigenvalues represent the frequencies of the normal modes, while the eigenvectors represent the corresponding amplitudes.
Normal modes are important because they allow us to understand the behavior of a complex system in a simplified manner. By determining the frequencies and amplitudes of the normal modes, we can predict how the system will respond to different types of disturbances.
In a coupled system, the normal modes can change depending on the strength of the coupling between the individual components. As the coupling increases, the frequencies and amplitudes of the normal modes may shift or even merge together, resulting in a more complex behavior of the system.
Yes, normal modes can be observed in many real-life systems, such as musical instruments, pendulums, and even molecules. In fact, the study of normal modes is essential in various fields of science, including physics, chemistry, and engineering.