NEET Oscillations — Set 14

Question 1

In SHM, what condition results in the potential energy being zero?

Accepted Answer

Potential energy $ U = \frac{1}{2} k x^2 $ is zero when displacement $ x = 0 $, which occurs at the mean position, where all energy is kinetic.

Question 2

Two identical springs ($ k = 50 \, \text{N/m} $) are attached to a $ 0.5 \, \text{kg} $ mass as in Fig. 13.14. What is the period?

Accepted Answer

Effective $ k_{\text{eff}} = 2k = 2 \times 50 = 100 \, \text{N/m} $. $ T = 2\pi \sqrt{\frac{m}{k_{\text{eff}}}} = 2\pi \sqrt{\frac{0.5}{100}} = 2\pi \sqrt{0.005} \approx 0.44 \, \text{s} $.

Question 3

A particle’s x-projection from circular motion is $ x = 10 \cos (2\pi t) $ (in m). What is its maximum acceleration?

Accepted Answer

Maximum acceleration: $ a_{\text{max}} = \omega^2 A $. $ A = 10 \, \text{m}, \omega = 2\pi \, \text{s}^{-1} $. $ a_{\text{max}} = (2\pi)^2 \times 10 \approx 39.48 \times 10 \approx 394.8 \, \text{m/s}^2 $.

NEET Physics: Oscillations — Practice Set 14

Q1. In SHM, what condition results in the potential energy being zero?

Q2. Two identical springs (\( k = 50 \, \text{N/m} \)) are attached to a \( 0.5 \, \text{kg} \) mass as in Fig. 13.14. What is the period?

Q3. A particle’s x-projection from circular motion is \( x = 10 \cos (2\pi t) \) (in m). What is its maximum acceleration?

Q4. A spring system has \( k = 800 \, \text{N/m}, m = 2 \, \text{kg} \). What is the maximum speed if amplitude is \( 5 \, \text{cm} \)?

Q5. Which condition must be satisfied for the potential energy in an SHM system to be expressible as a quadratic function of displacement?

Q6. What critical condition must the acceleration satisfy for a motion to be classified as simple harmonic?

Q7. A spring system has \( m = 0.3 \, \text{kg}, k = 120 \, \text{N/m}, A = 8 \, \text{cm} \). What is the potential energy at \( x = 4 \, \text{cm} \)?

Q8. A spring-mass system has \( m = 1.6 \, \text{kg}, k = 640 \, \text{N/m} \). What is its angular frequency?

Q9. Which of the following is a non-periodic motion? (\( \omega \) is a positive constant)

Q10. Two identical springs (\( k = 80 \, \text{N/m} \)) are attached to a \( 2 \, \text{kg} \) mass as in Fig. 13.14. What is the period?