Question #103278

The equation of motion of a particle moving along the x-axis is given by: d²x/dt² + 4dx/dt + 8x = 20cos2t. Calculate the amplitude, period and frequency of the oscillation after a long time has elapsed

Expert's answer

The equation of motion of a particle moving along the x-axis is given by

The solution

We obtain

Hence

Therefore:

amplitude "a=\\sqrt{5};"

period "T=\\frac{2\\pi}{\\omega}=\\pi;"

frequency "f=1\/T=1\/\\pi."

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