Oscillations and Waves > Forced and damped oscillations > Problem 3.5.31

Statement

When the forcing's frequency is small as compared to the oscillator's natural frequency, its displacement can be considered equal to , where is the oscillating force, is the rigidity of the oscillating system. At high frequencies of the forcing force, the acceleration of the oscillator can be considered equal to , where is the mass of the oscillator. Explain this.

Solution

Assuming that the forced oscillation dominates the free oscillation, when the particular solution is substituted into the equation of motion

we see that the relative magnitude of the two terms on the left are . If , then , so . On the other hand, if , then , so .

Answer

See the solution.