NEET Oscillations — Set 3

Question 1

What distinguishes the restoring force in a spring-mass system from that in a simple pendulum at small amplitudes?

Accepted Answer

The spring-mass system uses elastic force ($ F = -kx $), constant with displacement, while the pendulum’s force ($ F = -mg \sin \theta \approx -mg \theta $) derives from gravity and varies with angle.

Question 2

A particle in circular motion has its x-projection as $ x = 7 \cos (\pi t) $ (in m). What is its maximum speed?

Accepted Answer

Maximum speed: $ v_{\text{max}} = \omega A $. $ A = 7 \, \text{m}, \omega = \pi \, \text{s}^{-1} $. $ v_{\text{max}} = \pi \times 7 \approx 3.14 \times 7 \approx 21.98 \, \text{m/s} $.

Question 3

A simple pendulum has a period of $ 1.8 \, \text{s} $ on Earth ($ g = 9.8 \, \text{m/s}^2 $). What is its length?

Accepted Answer

$ T = 2\pi \sqrt{\frac{L}{g}} $. $ 1.8 = 2\pi \sqrt{\frac{L}{9.8}} \Rightarrow \sqrt{\frac{L}{9.8}} = \frac{1.8}{2\pi} \approx 0.2865 $. $ \frac{L}{9.8} = (0.2865)^2 \Rightarrow L \approx 9.8 \times 0.0821 \approx 0.805 \, \text{m} $.

NEET Physics: Oscillations — Practice Set 3

Q1. What distinguishes the restoring force in a spring-mass system from that in a simple pendulum at small amplitudes?

Q2. A particle in circular motion has its x-projection as \( x = 7 \cos (\pi t) \) (in m). What is its maximum speed?

Q3. A simple pendulum has a period of \( 1.8 \, \text{s} \) on Earth (\( g = 9.8 \, \text{m/s}^2 \)). What is its length?

Q4. A simple pendulum has a length of \( 0.4 \, \text{m} \) and oscillates with \( g = 9.8 \, \text{m/s}^2 \). What is its period?

Q5. A mass oscillates with \( v = -15 \cos (3t) \) (in m/s). What is its amplitude?

Q6. A pendulum of length \( 1.8 \, \text{m} \) oscillates with \( g = 10 \, \text{m/s}^2 \). What is its frequency?

Q7. A spring of \( k = 360 \, \text{N/m} \) has a \( 1.5 \, \text{kg} \) mass. If \( E = 1.8 \, \text{J} \), what is the amplitude?

Q8. In SHM, when does the particle experience its maximum restoring force?

Q9. A spring of \( k = 250 \, \text{N/m} \) has a \( 1 \, \text{kg} \) mass. If \( E = 1.25 \, \text{J} \), what is the amplitude?

Q10. A particle in SHM has \( x = 6 \cos (2\pi t + \frac{\pi}{4}) \) (in m). What is its speed at \( t = 0.25 \, \text{s} \)? (Take \( \sin 45^\circ = \frac{\sqrt{2}}{2} \))

Q11. What role does the phase constant play in differentiating two SHM systems with identical amplitude and frequency?

Q12. A particle’s x-projection from circular motion is \( x = 8 \cos (2\pi t) \) (in m). What is its maximum acceleration?

Q13. A spring-mass system oscillates with \( T = 0.9 \, \text{s} \) when \( m = 0.9 \, \text{kg} \). What is the spring constant?

Q14. A simple pendulum oscillates with a frequency of \( 0.5 \, \text{Hz} \) on Earth (\( g = 9.8 \, \text{m/s}^2 \)). What is its length?

Q15. A spring system has \( m = 1 \, \text{kg}, k = 100 \, \text{N/m}, A = 20 \, \text{cm} \). What is the potential energy at \( x = 0 \, \text{m} \)?