Damped harmonic oscillator being forced

[tomwilliam]

Homework Statement

A damped harmonic oscillator is being forced. I have to say whether it is direct forcing or forcing by displacement. I have the equation of motion which is expressed in terms of the particle's height above the equilibrium point and an expression for the force being applied.

Homework Equations

The Attempt at a Solution

I know that if it is forcing by displacement there should be a change in the length of the spring to which the particle is attached, but as my equation of motion is in terms of height above the equilibrium point, I'm not sure I can tell whether the spring length is constant or not. The forcing element is of the form C cos (omega t). I'm not sure whether I should be showing my answer to this question using a mathematical argument or based on the physical set up. Any help appreciated.

 

[anathema]

Based on the information provided, it is difficult to determine whether the harmonic oscillator is being directly forced or forced by displacement without knowing the specific values for the constants C and omega. However, in general, if the force being applied is a constant value, it is considered direct forcing. If the force is varying with time, it is considered forcing by displacement.

In terms of the physical setup, if the particle is attached to a spring that is fixed at one end, then the spring length would not change and the forcing would be considered direct. If the particle is attached to a spring that is free to move, then the spring length would change and the forcing would be considered by displacement.

In order to confirm your answer mathematically, you could solve the equation of motion for the position of the particle and see if it is directly proportional to the force being applied (direct forcing) or if it is proportional to the displacement of the particle from equilibrium (forcing by displacement).

I hope this helps. Best of luck with your problem!