NEET Oscillations — Set 13

Question 1

A pendulum has $ L = 1.2 \, \text{m}, g = 9.8 \, \text{m/s}^2 $. What is its angular frequency?

Accepted Answer

$ \omega = \sqrt{\frac{g}{L}} = \sqrt{\frac{9.8}{1.2}} \approx \sqrt{8.17} \approx 2.86 \, \text{rad/s} $.

Question 2

A simple pendulum has a period of $ 2.5 \, \text{s} $ on Earth ($ g = 9.8 \, \text{m/s}^2 $). What is its length?

Accepted Answer

$ T = 2\pi \sqrt{\frac{L}{g}} $. $ 2.5 = 2\pi \sqrt{\frac{L}{9.8}} \Rightarrow \sqrt{\frac{L}{9.8}} = \frac{2.5}{2\pi} \approx 0.398 $. $ \frac{L}{9.8} = (0.398)^2 \Rightarrow L \approx 9.8 \times 0.158 \approx 1.55 \, \text{m} $.

Question 3

A pendulum has $ L = 0.25 \, \text{m}, g = 10 \, \text{m/s}^2 $. What is its angular frequency?

Accepted Answer

$ \omega = \sqrt{\frac{g}{L}} = \sqrt{\frac{10}{0.25}} = \sqrt{40} \approx 6.32 \, \text{rad/s} $.

NEET Physics: Oscillations — Practice Set 13

Q1. A pendulum has \( L = 1.2 \, \text{m}, g = 9.8 \, \text{m/s}^2 \). What is its angular frequency?

Q2. A simple pendulum has a period of \( 2.5 \, \text{s} \) on Earth (\( g = 9.8 \, \text{m/s}^2 \)). What is its length?

Q3. A pendulum has \( L = 0.25 \, \text{m}, g = 10 \, \text{m/s}^2 \). What is its angular frequency?

Q4. A particle in SHM has \( x = 7 \sin (3\pi t + \frac{\pi}{3}) \) (in m). What is its speed at \( t = 0.5 \, \text{s} \)? (Take \( \cos 30^\circ = \frac{\sqrt{3}}{2} \))

Q5. A spring-mass system oscillates with \( T = 0.5 \, \text{s} \) when \( m = 0.5 \, \text{kg} \). What is the spring constant?

Q6. A mass oscillates with \( v = -12 \sin (6t) \) (in m/s). What is its amplitude?

Q7. In SHM, which quantity is directly proportional to the square of the angular frequency?

Q8. A spring-mass system has \( m = 2.5 \, \text{kg}, k = 1000 \, \text{N/m} \). What is its angular frequency?

Q9. What fundamental property of the restoring force distinguishes simple harmonic motion from other oscillatory motions?

Q10. A spring-mass system has \( m = 0.8 \, \text{kg}, k = 320 \, \text{N/m} \). If displaced by \( 5 \, \text{cm} \), what is the total energy?