NEET Oscillations — Set 1

Question 1

A spring of $ k = 300 \, \text{N/m} $ has a $ 1.5 \, \text{kg} $ mass. If $ E = 0.75 \, \text{J} $, what is the amplitude?

Accepted Answer

Total energy: $ E = \frac{1}{2} k A^2 $. $ 0.75 = 0.5 \times 300 \times A^2 \Rightarrow 0.75 = 150 A^2 \Rightarrow A^2 = 0.005 \Rightarrow A = \sqrt{0.005} \approx 0.071 \, \text{m} $.

Question 2

A spring of $ k = 180 \, \text{N/m} $ has a $ 0.9 \, \text{kg} $ mass. If $ E = 0.9 \, \text{J} $, what is the amplitude?

Accepted Answer

Total energy: $ E = \frac{1}{2} k A^2 $. $ 0.9 = 0.5 \times 180 \times A^2 \Rightarrow 0.9 = 90 A^2 \Rightarrow A^2 = 0.01 \Rightarrow A = 0.1 \, \text{m} $.

Question 3

A particle in SHM has $ x = 6 \sin (3t - \frac{\pi}{4}) $ (in m). What is its acceleration at $ t = 0 \, \text{s} $? (Take $ \cos 45^\circ = \frac{\sqrt{2}}{2} $)

Accepted Answer

Acceleration: $ a = -\omega^2 x $. $ \omega = 3 \, \text{s}^{-1}, x(0) = 6 \sin (-\frac{\pi}{4}) = -6 \sin \frac{\pi}{4} = -6 \times \frac{\sqrt{2}}{2} \approx -4.24 \, \text{m} $. $ a = -3^2 \times (-4.24) = 9 \times 4.24 \approx 38.16 \, \text{m/s}^2 $.

NEET Physics: Oscillations — Practice Set 1

Q1. A spring of \( k = 300 \, \text{N/m} \) has a \( 1.5 \, \text{kg} \) mass. If \( E = 0.75 \, \text{J} \), what is the amplitude?

Q2. A spring of \( k = 180 \, \text{N/m} \) has a \( 0.9 \, \text{kg} \) mass. If \( E = 0.9 \, \text{J} \), what is the amplitude?

Q3. A particle in SHM has \( x = 6 \sin (3t - \frac{\pi}{4}) \) (in m). What is its acceleration at \( t = 0 \, \text{s} \)? (Take \( \cos 45^\circ = \frac{\sqrt{2}}{2} \))

Q4. Which function represents periodic but not simple harmonic motion? (\( \omega \) is a positive constant)

Q5. In SHM, when is the magnitude of acceleration equal to zero?

Q6. A spring-mass system oscillates with \( T = 0.5 \, \text{s} \) when \( m = 0.5 \, \text{kg} \). What is the spring constant?

Q7. Which of the following motions is periodic but does not exhibit oscillatory behavior about a fixed point?

Q8. What distinguishes the restoring force in SHM from that in uniform circular motion?

Q9. A spring of \( k = 1000 \, \text{N/m} \) has a \( 2 \, \text{kg} \) mass. If \( E = 5 \, \text{J} \), what is the amplitude?

Q10. A pendulum of length \( 0.49 \, \text{m} \) oscillates with \( g = 9.8 \, \text{m/s}^2 \). What is its frequency?

Q11. A simple pendulum of length \( 0.25 \, \text{m} \) oscillates on Earth (\( g = 9.8 \, \text{m/s}^2 \)). What is its period?

Q12. A particle in SHM has \( x = 4 \cos (2t + \frac{\pi}{2}) \) (in m). What is its acceleration at \( t = 0 \, \text{s} \)?

Q13. A particle in SHM has \( x = 7 \cos (5t) \) (in m). What is its maximum acceleration?

Q14. A mass oscillates with \( v = -15 \sin (6t) \) (in m/s). What is its amplitude?

Q15. In SHM, if the particle’s velocity is zero, what can be inferred about its position relative to the equilibrium?