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.