• # question_answer A spring-mass suspension has a natural frequency of 40 rad/s. What is the damping ratio required if it is desired to reduce this frequency to 20 rad/s by adding a damper to it? A) $\frac{\sqrt{3}}{2}$                             B) $\frac{1}{2}$C) $\frac{1}{\sqrt{2}}$                             D) $\frac{1}{4}$

${{\omega }_{d}}={{\omega }_{n}}\sqrt{1-{{\zeta }^{2}}}$ $20=40\sqrt{1-{{\zeta }^{2}}}$ $1-{{\zeta }^{2}}=\frac{1}{4}$ ${{\zeta }^{2}}=\frac{3}{4},$ $\zeta =\frac{\sqrt{3}}{2}$