Oscillations - Result Question 12
15. Two simple harmonic motions of angular frequency 100 and $1000 rad s^{-1}$ have the same displacement amplitude. The ratio of their maximum accelerations is:
(a) $1: 10$
(c) $1: 10^{3}$
(b) $1: 10^{2}$
(d) $1: 10^{4}$
[2008]
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Answer:
Correct Answer: 15. (b)
Solution:
- (b) Maximum acceleration of a particle in the simple harmonic motion is directly proportional to the square of angular frequency i.e.,
i.e., $a \mu w^{2}$
$ \begin{aligned} & \therefore \frac{a_1}{a_2}=\frac{\omega_1^{2}}{\omega_2^{2}}=\frac{(100)^{2}}{(1000)^{2}}=\frac{1}{100} \\ & \Rightarrow a_1: a_2=1: 10^{2} . \end{aligned} $
