NEET Oscillations — Set 2

Question 1

Two identical springs ($ k = 60 \, \text{N/m} $) are attached to a $ 1.2 \, \text{kg} $ mass as in Fig. 13.14. What is the frequency?

Accepted Answer

Effective $ k_{\text{eff}} = 2k = 2 \times 60 = 120 \, \text{N/m} $. $ \omega = \sqrt{\frac{k_{\text{eff}}}{m}} = \sqrt{\frac{120}{1.2}} = \sqrt{100} = 10 \, \text{rad/s} $. $ v = \frac{\omega}{2\pi} = \frac{10}{2 \times 3.14} \approx 1.59 \, \text{Hz} $.

Question 2

A spring-mass system has $ m = 0.5 \, \text{kg}, k = 200 \, \text{N/m} $. If the amplitude is $ 4 \, \text{cm} $, what is the total energy?

Accepted Answer

Total energy: $ E = \frac{1}{2} k A^2 $. $ A = 0.04 \, \text{m}, k = 200 \, \text{N/m} $. $ E = 0.5 \times 200 \times (0.04)^2 = 0.5 \times 200 \times 0.0016 = 0.16 \, \text{J} $.

Question 3

A simple pendulum has a length of $ 0.9 \, \text{m} $ and oscillates with $ g = 9.8 \, \text{m/s}^2 $. What is its period?

Accepted Answer

Period: $ T = 2\pi \sqrt{\frac{L}{g}} = 2\pi \sqrt{\frac{0.9}{9.8}} \approx 2 \times 3.14 \sqrt{0.0918} \approx 1.9 \, \text{s} $.

NEET Physics: Oscillations — Practice Set 2

Q1. Two identical springs (\( k = 60 \, \text{N/m} \)) are attached to a \( 1.2 \, \text{kg} \) mass as in Fig. 13.14. What is the frequency?

Q2. A spring-mass system has \( m = 0.5 \, \text{kg}, k = 200 \, \text{N/m} \). If the amplitude is \( 4 \, \text{cm} \), what is the total energy?

Q3. A simple pendulum has a length of \( 0.9 \, \text{m} \) and oscillates with \( g = 9.8 \, \text{m/s}^2 \). What is its period?

Q4. A particle in SHM has an amplitude of \( 10 \, \text{cm} \) and a frequency of \( 2.5 \, \text{Hz} \). What is its maximum velocity? (Take \( \pi = 3.14 \))

Q5. What property of SHM allows its displacement to be expressed as a linear combination of sine and cosine functions?

Q6. A pendulum has \( L = 0.64 \, \text{m}, g = 9.8 \, \text{m/s}^2 \). What is its angular frequency?

Q7. A particle in SHM has \( x = 5 \sin (2t) \) (in m). What is its speed at \( x = 2.5 \, \text{m} \)?

Q8. Two identical springs (\( k = 70 \, \text{N/m} \)) are attached to a \( 1.4 \, \text{kg} \) mass as in Fig. 13.14. What is the frequency?

Q9. A particle in SHM has \( x = 5 \cos (2t + \frac{\pi}{4}) \) (in m). What is its acceleration at \( t = 0 \, \text{s} \)? (Take \( \cos 45^\circ = \frac{\sqrt{2}}{2} \))

Q10. Two identical springs (\( k = 100 \, \text{N/m} \)) are attached to a \( 1 \, \text{kg} \) mass as in Fig. 13.14. What is the period?

Q11. The projection of a particle in circular motion on the x-axis is \( x = 3 \cos (2\pi t) \) (in m). What is the radius of the circular path?

Q12. In an ideal SHM system, what happens to the kinetic energy as the particle approaches the extreme position?

Q13. A pendulum of length \( 0.8 \, \text{m} \) oscillates with \( g = 10 \, \text{m/s}^2 \). What is its frequency?

Q14. A mass of \( 3 \, \text{kg} \) is attached to a spring with \( k = 300 \, \text{N/m} \). If displaced by \( 15 \, \text{cm} \), what is the total energy?

Q15. A particle in SHM has \( x = 2 \sin (4t + \frac{\pi}{3}) \) (in m). What is its acceleration at \( t = 0 \, \text{s} \)? (Take \( \cos \frac{\pi}{3} = 0.5 \))