AP Physics C: Mechanics
7.2 Frequency and Period of SHM
7.1 Defining Simple Harmonic Motion (SHM)
A particle of mass \(m = 0.25 \text{ kg}\) moves along the \(x\)-axis in a conservative force field with potential energy given by \(U(x) = U_0 \cosh(bx)\), where \(U_0 = 4.0 \text{ J}\) and \(b = 3.0 \text{ m}^{-1}\). The particle is displaced slightly from its stable equilibrium position at \(x = 0\) and released from rest. Given that \(\dfrac{d}{dx}[\cosh(bx)] = b\sinh(bx)\), \(\dfrac{d}{dx}[\sinh(bx)] = b\cosh(bx)\), and \(\cosh(0) = 1\), what is the angular frequency of the resulting small-amplitude oscillations?
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