Question

For a damped harmonic oscillator of mass $250\,g$ , the values of spring constant $(k)$ and damping constant $(b)$ are $85\, N/m$ and $70\,g/s$ , respectively. What is the period of motion ?

• A. $2.5\,s$
• B. $5.0\,s$
• C. $0.34\,s$
• D. $7.2\,s$

Answer 1

Answer: (C)

$0.34\,s$

Answer 2

Given, mass of damped harmonic oscillator
$m = 250\,g = \frac{250}{1000} \,kg$
$= \frac{1}{4} kg$
Spring constant $(k) = 85 \,Nm^{-1}$
Damping constant $(b) = 70 \,gs^{-1} = 0.07 \,kgs^{-1}$
Frequency of damped oscillator
$f = \frac{1}{2n} \sqrt{\frac{k}{m} -\frac{b^{2}}{4m^{2}}}$
$= \frac{1}{2\times3.14}\sqrt{\frac{85}{\frac{1}{4}}-0.07\times\frac{0.07}{4\times\frac{1}{4}\times \frac{1}{4}}}$
$= \frac{1}{ 2\times 3.14} \sqrt{340 - 0.0196}$
$= \frac{1}{2\times 3.14} \times18.43$
$= 2.93$
Now $T = \frac{1}{f} = \frac{1}{2.93}$
$= 0.34 \,s$