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A partical of mass m is located in a uni...

A partical of mass `m` is located in a unidimensionnal potential field where potentical energy of the partical depends on the coordinates `x as: U (x) = U_(0) (1 - cos Ax), U_(0)` and A constants.
Find the period of small oscillation that the partical performs about the equilibrium position.

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To find the period of small oscillation of a particle in a unidimensional potential field defined by the potential energy function \( U(x) = U_0 (1 - \cos(Ax)) \), we can follow these steps: ### Step 1: Identify the Equilibrium Position The equilibrium position occurs where the force acting on the particle is zero. The force can be derived from the potential energy as: \[ F(x) = -\frac{dU}{dx} \] Calculating the derivative: ...
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