Question

A student working with a spring mass systems finds the values of mass, spring constant and damping constant in CGS unit as $90,4.5\times {10}^{+3}$ and $180$ respectively. What will be the time period of the spring mass system?

• A. $\frac{2\pi }{7}$
• B. $14\pi$
• C. $\pi$
• D. $\frac{2\pi }{\sqrt{50}}$

Answer 1

The correct option is A $\frac{2\pi }{7}$

For damped oscillation,
$\omega =\sqrt{\frac{K}{m}-\frac{b_1^2}{4m^2}}$
$\omega =\sqrt{\frac{4500}{90}-\frac{180\times 180}{4\times 90\times 90}}=\sqrt{50-1}=7$
Time period $=\frac{2\pi }{7}$ sec.