Wave Mechanics Question 603
Question: A particle of mass m is attached to a spring (of spring constant k) and has a natural angular frequency $ {\omega _{0}} $ . An external force F (t) proportional to $ \cos ,\omega t(\omega \ne {\omega _{0}}) $ is applied to the oscillator. The displacement of the oscillator will be proportional to
Options:
A) $ \frac{1}{m(\omega _{0}^{2}+{{\omega }^{2}})} $
B) $ \frac{1}{m(\omega _{0}^{2}-{{\omega }^{2}})} $
C) $ \frac{m}{\omega _{0}^{2}-{{\omega }^{2}}} $
D) $ \frac{m}{(\omega _{0}^{2}+{{\omega }^{2}})} $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] $ x=A,\sin (\omega t+\phi ) $
Where $ A=\frac{F _{0}}{m\sqrt{{{(\omega _{0}^{2}-{{\omega }^{2}})}^{2}}}}=\frac{F _{0}}{m(\omega _{0}^{2}-{{\omega }^{2}})} $
Here damping effect is considered to be zero
$ \
Therefore ,x\propto \frac{1}{m({\omega _{0}}^{2}-{{\omega }^{2}})} $
BETA
