Question

Two simple harmonic motions of angular frequency $100$ and $1000 \,rad \,s^1$ have the same displacement amplitude. The ratio of their maximum acceleration is

• A. $1 : 10^3 $
• B. $1 : 10^4 $
• C. $1 : 10 $
• D. $1 : 10^2$

Answer 1

Answer: (D)

$\omega_{1}=100 \,rad\, s ^{-1} ; \omega_{2}=1000\,rad \,s ^{-1} $
Maximum acceleration of $(1)=-\omega_{1}^{2} A$
Maximum acceleration of $(2)=-\omega_{2}^{2} A$
$\therefore \frac{\text{accln}(1)}{\text{accln}(2)}=\frac{\omega_{1}^{2}}{\omega_{2}^{2}}=\frac{(100)^{2}}{(1000)^{2}}=\frac{1}{100}$
$a(1): a(2)=1: 100 $