NEET Oscillations — Set 6

Question 1

Which of the following represents periodic motion but not SHM? ($ \omega $ is a positive constant)

Accepted Answer

(a) $ 4 \cos (\omega t) $: SHM. (b) $ \sin \omega t + \sin 2\omega t $: Periodic (period $ \frac{2\pi}{\omega} $), not SHM (multiple frequencies). (c) $ 3 \sin (\omega t - \frac{\pi}{3}) $: SHM. (d) $ e^{\omega t} $: Not periodic.

Question 2

A spring system has $ m = 1.2 \, \text{kg}, k = 480 \, \text{N/m}, A = 6 \, \text{cm} $. What is the potential energy at $ x = 3 \, \text{cm} $?

Accepted Answer

Potential energy: $ U = \frac{1}{2} k x^2 $. $ k = 480 \, \text{N/m}, x = 0.03 \, \text{m} $. $ U = 0.5 \times 480 \times (0.03)^2 = 0.5 \times 480 \times 0.0009 = 0.216 \, \text{J} $.

Question 3

What is the primary reason a simple pendulum’s period increases at higher altitudes?

Accepted Answer

The period $ T = 2\pi \sqrt{\frac{L}{g}} $ increases as $ g $ (acceleration due to gravity) decreases with altitude, inversely affecting the period.

NEET Physics: Oscillations — Practice Set 6

Q1. Which of the following represents periodic motion but not SHM? (\( \omega \) is a positive constant)

Q2. A spring system has \( m = 1.2 \, \text{kg}, k = 480 \, \text{N/m}, A = 6 \, \text{cm} \). What is the potential energy at \( x = 3 \, \text{cm} \)?

Q3. What is the primary reason a simple pendulum’s period increases at higher altitudes?

Q4. A mass of \( 2 \, \text{kg} \) on a spring has \( k = 800 \, \text{N/m} \) and \( A = 10 \, \text{cm} \). What is the kinetic energy at \( x = 5 \, \text{cm} \)?

Q5. A mass oscillates with \( v = -10 \sin (5t) \) (in m/s). What is its amplitude?

Q6. A particle’s x-projection from circular motion is \( x = 5 \cos (2t) \) (in m). What is its maximum speed?

Q7. A simple pendulum has a length of \( 0.81 \, \text{m} \) and oscillates with \( g = 9.8 \, \text{m/s}^2 \). What is its period?

Q8. A simple pendulum has a length of \( 1.6 \, \text{m} \) and oscillates with \( g = 9.8 \, \text{m/s}^2 \). What is its period?

Q9. A particle in SHM has an amplitude of \( 6 \, \text{cm} \) and a frequency of \( 3 \, \text{Hz} \). What is its maximum velocity? (Take \( \pi = 3.14 \))

Q10. Which function represents SHM? (\( \omega \) is a positive constant)

Q11. A particle’s displacement is \( x = 8 \sin (2\pi t - \frac{\pi}{3}) \) (in m). What is its velocity at \( t = 0.25 \, \text{s} \)? (Take \( \cos 30^\circ = \frac{\sqrt{3}}{2} \))

Q12. A mass of \( 0.8 \, \text{kg} \) on a spring with \( k = 200 \, \text{N/m} \) has \( A = 10 \, \text{cm} \). What is the kinetic energy at \( x = 5 \, \text{cm} \)?

Q13. A spring system has \( m = 0.4 \, \text{kg}, k = 160 \, \text{N/m}, A = 7 \, \text{cm} \). What is the potential energy at \( x = 3.5 \, \text{cm} \)?

Q14. What physical property of a simple pendulum primarily governs its oscillatory behavior?

Q15. In SHM, which quantity is maximized when the particle’s acceleration is at its peak?