NEET Oscillations — Set 11

Question 1

A spring of $ k = 400 \, \text{N/m} $ is attached to a $ 1 \, \text{kg} $ mass. What is the angular frequency?

Accepted Answer

$ \omega = \sqrt{\frac{k}{m}} = \sqrt{\frac{400}{1}} = 20 \, \text{rad/s} $.

Question 2

A mass of $ 0.5 \, \text{kg} $ on a spring with $ k = 50 \, \text{N/m} $ has $ A = 20 \, \text{cm} $. What is the kinetic energy at $ x = 10 \, \text{cm} $?

Accepted Answer

Total energy: $ E = \frac{1}{2} k A^2 = 0.5 \times 50 \times (0.2)^2 = 1 \, \text{J} $. Potential energy: $ U = \frac{1}{2} k x^2 = 0.5 \times 50 \times (0.1)^2 = 0.25 \, \text{J} $. Kinetic energy: $ K = E - U = 1 - 0.25 = 0.75 \, \text{J} $.

Question 3

A particle in SHM has an amplitude of $ 8 \, \text{cm} $ and a period of $ 0.4 \, \text{s} $. What is its maximum velocity? (Take $ \pi = 3.14 $)

Accepted Answer

Maximum velocity: $ v_{\text{max}} = A \omega $. $ \omega = \frac{2\pi}{T} = \frac{2 \times 3.14}{0.4} = 15.7 \, \text{rad/s} $. $ A = 0.08 \, \text{m} $. $ v_{\text{max}} = 0.08 \times 15.7 = 1.256 \, \text{m/s} $.

NEET Physics: Oscillations — Practice Set 11

Q1. A spring of \( k = 400 \, \text{N/m} \) is attached to a \( 1 \, \text{kg} \) mass. What is the angular frequency?

Q2. A mass of \( 0.5 \, \text{kg} \) on a spring with \( k = 50 \, \text{N/m} \) has \( A = 20 \, \text{cm} \). What is the kinetic energy at \( x = 10 \, \text{cm} \)?

Q3. A particle in SHM has an amplitude of \( 8 \, \text{cm} \) and a period of \( 0.4 \, \text{s} \). What is its maximum velocity? (Take \( \pi = 3.14 \))

Q4. A spring of \( k = 250 \, \text{N/m} \) has a \( 2.5 \, \text{kg} \) mass. If \( E = 1.25 \, \text{J} \), what is the amplitude?

Q5. A simple pendulum has a length of \( 1.69 \, \text{m} \) and oscillates with \( g = 9.8 \, \text{m/s}^2 \). What is its period?

Q6. In SHM, if the displacement is zero, what can be inferred about the acceleration?

Q7. A simple pendulum has a period of \( 3 \, \text{s} \) on Earth. What will be its period on a planet where \( g = 2.45 \, \text{m/s}^2 \)? (Take \( g_{\text{Earth}} = 9.8 \, \text{m/s}^2 \))

Q8. Which periodic motion lacks a restoring force directed towards a fixed equilibrium point?

Q9. Which function represents periodic motion but not SHM? (\( \omega \) is a positive constant)

Q10. A particle’s x-projection from circular motion is \( x = 9 \cos (\pi t) \) (in m). What is its maximum speed?