Question

A particle oscillating under a force $ \overrightarrow{F}=-k\overrightarrow{x}-b\overrightarrow{v} $ is a(k and b are constants)

• A. simple harmonic oscillator
• B. non linear oscillator
• C. damped oscillator
• D. forced oscillator
• E. linear oscillator

Answer 1

Answer: (C)

In damped oscillation, suppose, an oscillator having mass M and force constant k is acted upon by a resistive force
$ {{F}_{0}} $ .
It is found that the resistive force is proportional to the velocity (v) of the oscillator. That is $ {{F}_{b}}=bv, $ where b is a constant and is called the damping factor. If $ x $ be the instantaneous displacement of the oscillator, then
$ M\frac{{{d}^{2}}x}{d{{t}^{2}}}=-kx-bv $
So, a particle oscillating under a force
$ \overrightarrow{F}=-k\overrightarrow{x}-b\overrightarrow{v} $ is a damped oscillator.