Question 222: Oscillations

Question

Two simple harmonic motions of angular frequency $300 \mathrm{rad} / \mathrm{s}$ and $3000 \mathrm{rad} / \mathrm{s}$ have same amplitude. The ratio of their maximum accelerations is

Accepted Answer

Let amplitude of both oscillations be $A$.
Let angular frequencies be
$\omega_{1} = 300 	ext{ rad/s}$
$\omega_{2} = 3000 	ext{ rad/s}$
For a simple harmonic motion, maximum acceleration is given by:
$$ a_{	ext{max}} = \omega^2 A $$
Maximum acceleration for each:
First motion:
$$   a_{1,	ext{max}} = \omega_1^2 A = (300)^2 A = 90000A   $$
Second motion:
$$   a_{2,	ext{max}} = \omega_2^2 A = (3000)^2 A = 9000000A   $$
Ratio of maximum accelerations:
$$ \frac{a_{1,	ext{max}}}{a_{2,	ext{max}}} = \frac{90000A}{9000000A} = \frac{1}{100} $$
Therefore,
$$ a_{1,	ext{max}} : a_{2,	ext{max}} = 1 : 100 $$
So, the correct answer is:
Option B: $1 : 10^2$

Answer

$1: 10$

Answer

$1: 10^2$

Answer

$1: 10^3$

Answer

$1: 10^4$

Oscillations

Two simple harmonic motions of angular frequency 300 \mathrm{rad} / \mathrm{s} and 3000 \mathrm{rad} / \mathrm{s} have same amplitude. The ratio of their maximum accelerations is

Choose the correct answer: