Wave Mechanics Question 549
Question: The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is $ 10{{s}^{-1}} $ . At, t = 0 the displacement is 5 m. The initial phase is $ \frac{\pi }{4} $ . What is the maximum acceleration?
Options:
A) $ 500m/s^{2} $
B) $ 500,\sqrt{2},m/s^{2} $
C) $ 750m/s^{2} $
D) $ 750,\sqrt{2},m/s^{2} $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Given that, $ \frac{{A _{\max }}}{{V _{\max }}}=10i.c.,,\omega =10{{s}^{-1}} $ Displacement is given by $ x=a,\sin ,(\omega t+\pi /4) $
$ at,t=0,,x=5;5=a,\sin ,45^{o}\Rightarrow a=5\sqrt{2} $
$ {A _{\max }}=a{{\omega }^{2}}=500\sqrt{2,}m/s^{2} $
BETA
