Use the method of renormalization to determine a two-term frequency-amplitude relationship for a block of mass (m)
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Use the method of renormalization to determine a two-term frequency-amplitude relationship for a block of mass \(m\) attached to a spring with a quadratic nonlinearity. When nondimensionalized the differential equation governing free vibrations of the system is
\[ \ddot{x}+\omega^{2} x+\epsilon x^{2}=0 \quad \epsilon \ll 1 \]
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