, I'm not supposed/allowed to give direct answers !First, you need to know what the "small" displacement is. Let's say you lift the center by an amount ##h##, so the center of the string is at ##(\frac L 2,h)##. Now just find the equation of the two straight line segments forming the triangular displacement. Also, I would ignore BvU's answer which is a) discontinuous and b) partially parabolic.nazmus sakib said:
No, it was just a typo. I (of course) meantLCKurtz said:
A Fourier sine series is a mathematical representation of a periodic function as an infinite sum of sine functions with different frequencies and amplitudes. It is used to analyze and approximate various types of periodic phenomena, including sound and electromagnetic waves.
A triangular wave is a periodic waveform that has a triangular shape, with equal slopes in both positive and negative directions. It is commonly used to represent oscillating signals in electronics and is also found in natural phenomena, such as ocean waves.
A Fourier sine series can be used to represent a triangular wave by decomposing it into a sum of sine functions with different frequencies and amplitudes that together create the triangular shape. This allows for a more precise analysis and manipulation of the triangular wave.
A finite string refers to a physical object, such as a guitar string, that can be modeled as a one-dimensional string with a finite length. In the context of Fourier sine series, a finite string is used as the medium on which the triangular wave is being represented and analyzed.
The applications of Fourier sine series for a triangular wave on a finite string are numerous. Some examples include analyzing the sound produced by vibrating guitar strings, predicting the behavior of ocean waves, and designing electronic circuits that use triangular wave signals.