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Student Solution Manual for Mathematical Methods for Physics and Engineering, Third Edition by M. P. Hobson, K. F. Riley

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15

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Higher-order ordinary differential equations

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15.1  A simple harmonic oscillator, of mass m and natural frequency ω0, experiences an oscillating driving force f(t) = ma cos ωt. Therefore, its equation of motion is

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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 ω0.

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

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