3. Consider a 1-dimensional pendulum of length and mass m oscillating around its equilibrium position, subject...

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3. Consider a 1-dimensional pendulum of length and mass m oscillating around its equilibrium position, subject to the force of gravity. Let us denote the acceleration due to gravity as g. Show that, in a regime of small oscillations, the potential the system is subject to is that of a harmonic oscillator and write the energy eigenvalues of the system. [4] 3. Consider a 1-dimensional pendulum of length and mass m oscillating around its equilibrium position, subject to the force of gravity. Let us denote the acceleration due to gravity as g. Show that, in a regime of small oscillations, the potential the system is subject to is that of a harmonic oscillator and write the energy eigenvalues of the system. [4]

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