7. A simple harmonic oscillator, of mass m and natural frequency wo, experiences an oscillating driving force f(t) = ma cos wt. Therefore, its equation of motion is d²x + wix = a cos wt, %3D dt² 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 w is approximately, but not exactly, equal to wo.
7. A simple harmonic oscillator, of mass m and natural frequency wo, experiences an oscillating driving force f(t) = ma cos wt. Therefore, its equation of motion is d²x + wix = a cos wt, %3D dt² 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 w is approximately, but not exactly, equal to wo.
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Simple harmonic motion
Transcribed Image Text:7.
A simple harmonic oscillator, of mass m and natural frequency wo, experiences
an oscillating driving force f(t) = ma cos wt. Therefore, its equation of motion is
d²x
+ wix = a cos wt,
%3D
dt²
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 w is approximately, but not exactly, equal
to wo.
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