NEET Oscillations — Set 8

Question 1

A mass oscillates with $ v = -10 \cos (5t) $ (in m/s). What is its amplitude?

Accepted Answer

Velocity: $ v = -\omega A \sin (\omega t) $, but given $ v = -10 \cos (5t) $. $ \omega = 5 \, \text{s}^{-1}, v_{\text{max}} = \omega A = 10 \Rightarrow A = \frac{10}{5} = 2 \, \text{m} $.

Question 2

A pendulum of length $ 1.5 \, \text{m} $ oscillates with $ g = 10 \, \text{m/s}^2 $. What is its period?

Accepted Answer

$ T = 2\pi \sqrt{\frac{L}{g}} = 2\pi \sqrt{\frac{1.5}{10}} = 2\pi \sqrt{0.15} \approx 2 \times 3.14 \times 0.387 \approx 2.43 \, \text{s} $.

Question 3

A particle in SHM has a displacement $ x = 3 \cos (4t + \frac{\pi}{3}) $ (in meters). What is its acceleration at $ t = 0 \, \text{s} $?

Accepted Answer

Acceleration: $ a(t) = -\omega^2 x(t) $. Here, $ \omega = 4 \, \text{s}^{-1}, x(0) = 3 \cos (\frac{\pi}{3}) = 3 \times 0.5 = 1.5 \, \text{m} $. $ a(0) = -4^2 \times 1.5 = -16 \times 1.5 = -24 \, \text{m/s}^2 $.

NEET Physics: Oscillations — Practice Set 8

Q1. A mass oscillates with \( v = -10 \cos (5t) \) (in m/s). What is its amplitude?

Q2. A pendulum of length \( 1.5 \, \text{m} \) oscillates with \( g = 10 \, \text{m/s}^2 \). What is its period?

Q3. A particle in SHM has a displacement \( x = 3 \cos (4t + \frac{\pi}{3}) \) (in meters). What is its acceleration at \( t = 0 \, \text{s} \)?

Q4. A simple pendulum has a period of \( 1.4 \, \text{s} \) on Earth (\( g = 9.8 \, \text{m/s}^2 \)). What is its length?

Q5. A spring-mass system has \( m = 2.25 \, \text{kg}, k = 900 \, \text{N/m} \). What is its period?

Q6. A spring system has \( m = 0.25 \, \text{kg}, k = 100 \, \text{N/m}, A = 8 \, \text{cm} \). What is the potential energy at \( x = 4 \, \text{cm} \)?

Q7. A mass of \( 1.2 \, \text{kg} \) on a spring with \( k = 300 \, \text{N/m} \) has \( A = 8 \, \text{cm} \). What is the kinetic energy at \( x = 4 \, \text{cm} \)?

Q8. Which characteristic of SHM ensures that the motion repeats exactly after a fixed interval?

Q9. A particle in SHM has \( x = 4 \sin (3t) \) (in m). What is its speed at \( x = 2 \, \text{m} \)?

Q10. A particle in SHM has \( a = -81 x \) (in SI units). What is its frequency?

Q11. Why does the period of a simple pendulum remain constant regardless of the bob’s material?

Q12. A simple pendulum has a length of \( 1.44 \, \text{m} \) and oscillates with \( g = 9.8 \, \text{m/s}^2 \). What is its period?

Q13. A particle in SHM has \( a = -49 x \) (in SI units). What is its period?

Q14. A spring-mass system oscillates with \( T = 1.0 \, \text{s} \) when \( m = 0.4 \, \text{kg} \). What is the spring constant?

Q15. A particle in SHM has \( x = 6 \cos (4t) \) (in m). What is its maximum acceleration?