Word Count : 415

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The given equation represents a second-order ordinary differential equation describing the motion of an undamped forced vibration system: \[ m\ddot{u} + k u = F_0 \cos(\omega t) \] with initial conditions: \[ u(0) = 0, \quad \dot{u}(0) = 1 \] ### Step 1: Rewrite the Equation in Standard Form Dividing through by \( m \): \[ \ddot{u} + \frac{k}{m} u = \frac{F_0}{m} \cos(\omega t) \] Define the natural frequency: ________ ___ _________ _____ __________ _________ ____.
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