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An oscillating pendulum, as shown in Fig. P12.7, consists of a mass mattached to a massless spring of spring constant k and of relaxed

An oscillating pendulum, as shown in Fig. P12.7, consists of a mass mattached to a massless spring of spring constant k and of relaxed length l. Find Lagrange's equations of motion. Under what conditions will this system reduce to (a) a simple pendulum, and (b) a linear harmonic oscillator? Figure P12.7

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