*15*

*Higher-order ordinary differential equations*

**15.1***A simple harmonic oscillator, of mass* *m* *and natural frequency* *ω*_{0}*, experiences an oscillating driving force* *f*(*t*) = *ma* cos *ωt**. Therefore, its equation of* *motion is*

*where x is its position. Given that at t* = 0 *we have x* = *dx/dt* = 0*, find the function x*(*t*)*. Describe the solution if ω is approximately, but not exactly, equal to ω*_{0}.

To find the full solution given the initial conditions, we need the ...

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