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A mechanical or electronic system or device that works on the principles of oscillation, that is a periodic fluctuation between two things based on changes in energy. These range from abstract models such as a harmonic oscillator to electrical devices such as an LC circuit.
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Issues carrying out Taylor Expansion for small oscillations
I will first describe how I understand the question: You have a differential equation, namely $\ddot{\theta}+\left(\frac{g}{l}-\dot{\phi}^2\cos(\theta)\right)\sin(\theta)=0$. You mention that you want …