Question

A weight is attached to a spring suspended vertically from a ceiling. When a driving force is applied to the system, the weight moves vertically from its equilibrium position, and this motion is modeled by ?

Answer 1

Step-by-step explanation:

This is a simple harmonic motion, produced by the action of a driving force that is directly proportional to the position of the body. Its position is described as a function of time by a sinusoidal function. According to Newton's second law and Hooke's law:

`F=m(d^2x)/(dt^2)\\F=-kx`

Here m is the object's mass, k is the spring constant and x is the displacement from the equilibrium position.

`m(d^2x)/(dt^2)=-kx\\(d^2x)/(dt^2)=-\omega_0^2x\\x=Asin(\omega_0 t-\phi)`

With
`\omega_0=\sqrt{(k)/(m)}`, called natural frequency, A is the amplitude, that is the maximum displacement for the equilibrium position and
`\phi` is the initial phase.