Question

Two simple harmonic motions of angular frequency $100$ and $1000rad{s}^1$ 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)

${\omega }_1=100rad{s}^{-1};{\omega }_2=1000rad{s}^{-1}$
Maximum acceleration of $(1)=-{\omega }_1^{2}A$
Maximum acceleration of $(2)=-{\omega }_2^{2}A$
$\therefore \frac{\text{accln}(1)}{\text{accln}(2)}=\frac{{\omega }_1^2}{{\omega }_2^2}=\frac{(100{)}^2}{(1000{)}^2}=\frac{1}{100}$
$a(1):a(2)=1:100$