Question

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

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

Answer 1

The correct option is B $1:{10}^2$

Acceleration of simple harmonic motion is
$a_{max}=-{\omega }^{2}A$
or $\frac{{\left(a_{max}\right)}_1}{{\left(a_{max}\right)}_2}=\frac{{\omega }_1^2}{{\omega }_2^2}$ (as $A$ remains same)
or $\frac{{\left(a_{max}\right)}_1}{{\left(a_{max}\right)}_2}=\frac{{\left(100\right)}^2}{{\left(1000\right)}^2}={\left(\frac{1}{10}\right)}^2$
$=1:{10}^2$