NEET Oscillations — Set 7

Question 1

In SHM, what is the phase relationship between displacement and acceleration?

Accepted Answer

Displacement ($ x = A \cos (\omega t + \phi) $) and acceleration ($ a = -\omega^2 A \cos (\omega t + \phi) $) are 180° ($ \pi $ radians) out of phase, as acceleration is the negative of displacement.

Question 2

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

Accepted Answer

Velocity: $ v = \pm \omega \sqrt{A^2 - x^2} $. $ A = 4 \, \text{m}, \omega = 3 \, \text{s}^{-1}, x = 2 \, \text{m} $. $ v = 3 \sqrt{4^2 - 2^2} = 3 \sqrt{16 - 4} = 3 \sqrt{12} = 6\sqrt{3} \approx 10.39 \, \text{m/s} $.

Question 3

A spring-mass system has $ m = 1.8 \, \text{kg}, k = 720 \, \text{N/m} $. What is its frequency?

Accepted Answer

Angular frequency: $ \omega = \sqrt{\frac{k}{m}} = \sqrt{\frac{720}{1.8}} = \sqrt{400} = 20 \, \text{rad/s} $. Frequency: $ v = \frac{\omega}{2\pi} = \frac{20}{2 \times 3.14} \approx 3.18 \, \text{Hz} $.

NEET Physics: Oscillations — Practice Set 7

Q1. In SHM, what is the phase relationship between displacement and acceleration?

Q2. A particle in SHM has \( x = 4 \cos (3t) \) (in m). What is its speed when \( x = 2 \, \text{m} \)?

Q3. A spring-mass system has \( m = 1.8 \, \text{kg}, k = 720 \, \text{N/m} \). What is its frequency?

Q4. A particle in SHM has \( a = -100 x \) (in SI units). What is its frequency?

Q5. A particle’s acceleration in SHM is \( a = -25 x \) (in SI units). What is its frequency?

Q6. A pendulum of length \( 2.5 \, \text{m} \) oscillates with \( g = 10 \, \text{m/s}^2 \). What is its frequency?

Q7. A pendulum of length \( 1.21 \, \text{m} \) oscillates with \( g = 9.8 \, \text{m/s}^2 \). What is its frequency?

Q8. A mass oscillates with \( v = -12 \cos (4t) \) (in m/s). What is its amplitude?

Q9. Which factor in a spring-mass system directly influences the stiffness of the restoring force?

Q10. In SHM, if the displacement is at its maximum positive value, what can be said about the direction of the acceleration?

Q11. A pendulum of length \( 1.0 \, \text{m} \) oscillates with \( g = 10 \, \text{m/s}^2 \). What is its frequency?

Q12. A pendulum bob oscillates with \( \theta = 0.1 \, \text{rad} \). If \( L = 1 \, \text{m}, g = 10 \, \text{m/s}^2 \), what is the maximum speed?

Q13. A particle in SHM has \( x = 3 \sin (2t) \) (in m). What is its speed at \( x = 1.5 \, \text{m} \)?

Q14. What is a distinguishing feature of oscillatory motion compared to general periodic motion?

Q15. A particle in SHM has \( x = 5 \sin (4t - \frac{\pi}{6}) \) (in m). What is its acceleration at \( t = 0.25 \, \text{s} \)? (Take \( \cos 30^\circ = \frac{\sqrt{3}}{2} \))