Wave Mechanics Question 609
Question: The amplitude of velocity of a particle is given by, $ V _{m}=V _{0}/(a{{\omega }^{2}}-b\omega +c) $ where $ V _{0} $ , a, b and c are positive: The condition for a single resonant frequency is
Options:
A) $ b^{2}<4ac $
B) $ b^{2}=4ac $
C) $ b^{2}=5ac $
D) $ b^{2}=7ac $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] $ V _{m}=V _{0}/(a{{\omega }^{2}}-b\omega +c) $ If there is a single resonant frequency, then this equation should be satisfied for only one that particular resonant frequency, hence $ a{{\omega }^{2}}-b\omega +c=0 $ will have equal roots therefore; $ D=0\Rightarrow {{(-b)}^{2}}-4ac=0\Rightarrow b^{2}=4ac $ particular resonant frequency, hence $ a{{\omega }^{2}}-b\omega +c=0 $ will have equal roots therefore; $ D=0\Rightarrow {{(-b)}^{2}}-4ac=0\Rightarrow b^{2}=4ac $
BETA
