NEET Oscillations — Set 15

Question 1

What happens to the frequency of a spring-mass system if the spring constant is quadrupled and the mass is halved?

Accepted Answer

Frequency $ v = \frac{1}{2\pi} \sqrt{\frac{k}{m}} $. If $ k' = 4k $ and $ m' = \frac{m}{2} $, then $ v' = \frac{1}{2\pi} \sqrt{\frac{4k}{m/2}} = \frac{1}{2\pi} \sqrt{\frac{8k}{m}} = \sqrt{8} \cdot v = 2\sqrt{2} \cdot v $, doubling the original frequency by $ \sqrt{2} $.

Question 2

A spring-mass system has $ m = 1.25 \, \text{kg}, k = 500 \, \text{N/m} $. What is its angular frequency?

Accepted Answer

$ \omega = \sqrt{\frac{k}{m}} = \sqrt{\frac{500}{1.25}} = \sqrt{400} = 20 \, \text{rad/s} $.

Question 3

Which function represents simple harmonic motion? ($ \omega $ is a positive constant)

Accepted Answer

SHM requires $ a = -\omega^2 x $: (a) $ \cos \omega t + \sin 2\omega t $: Not SHM (mixed frequencies). (b) $ 4 \sin (\omega t + \frac{\pi}{6}) $: $ a = -4\omega^2 \sin (\omega t + \frac{\pi}{6}) = -\omega^2 x $, SHM. (c) $ e^{\omega t} $: Not periodic. (d) $ \sin^2 \omega t $: Periodic, not SHM.

NEET Physics: Oscillations — Practice Set 15

Q1. What happens to the frequency of a spring-mass system if the spring constant is quadrupled and the mass is halved?

Q2. A spring-mass system has \( m = 1.25 \, \text{kg}, k = 500 \, \text{N/m} \). What is its angular frequency?

Q3. Which function represents simple harmonic motion? (\( \omega \) is a positive constant)

Q4. A particle’s x-projection from circular motion is \( x = 6 \cos (3t) \) (in m). What is its maximum acceleration?

Q5. Which function represents SHM? (\( \omega \) is a positive constant)

Q6. A simple pendulum has a frequency of \( 0.25 \, \text{Hz} \) on Earth (\( g = 9.8 \, \text{m/s}^2 \)). What is its length?

Q7. Which statement best explains why uniform circular motion is not considered oscillatory despite being periodic?

Q8. What is the effect on the frequency of a simple pendulum if it is taken to a planet where gravity is one-fourth that of Earth?

Q9. What distinguishes the oscillatory nature of a pendulum from the periodic motion of a planet in orbit?

Q10. A pendulum oscillates with a period of \( 1.5 \, \text{s} \) on Earth (\( g = 9.8 \, \text{m/s}^2 \)). What is its length?