Question

An unhappy mouse of mass $m_0$, moving on the end of a spring of spring constant p is acted upon by a damping force $F_x=-b{v}_x$. For what value of b the motion is critically damped?

• A. $b=\sqrt{\frac{p}{m_0}}$
• B. $b=2\sqrt{p{m}_0}$
• C. $b=\sqrt{\frac{p^2}{2m_0}}$
• D. $b=\sqrt{\frac{p}{2m_0}}$

Answer 1

Answer: (B)

$b=2\sqrt{p{m}_0}$

The motion of the mouse is critically damped if $\frac{b}{2m_0}={\omega }_o$
$\Rightarrow \frac{b}{2m_0}=\sqrt{\frac{p}{m_0}}\Rightarrow b=2\sqrt{p{m}_0}$