NEET Oscillations — Set 19

Question 1

A simple pendulum has a period of $ 1 \, \text{s} $ on Earth ($ g = 9.8 \, \text{m/s}^2 $). What is its period on the Moon ($ g = 1.63 \, \text{m/s}^2 $)?

Accepted Answer

$ T \propto \frac{1}{\sqrt{g}} $. $ \frac{T_{\text{Moon}}}{T_{\text{Earth}}} = \sqrt{\frac{g_{\text{Earth}}}{g_{\text{Moon}}}} = \sqrt{\frac{9.8}{1.63}} \approx \sqrt{6} \approx 2.45 $. $ T_{\text{Moon}} = 1 \times 2.45 \approx 2.45 \, \text{s} $.

Question 2

For a motion to be simple harmonic, the restoring force must satisfy which condition when plotted against displacement?

Accepted Answer

In SHM, the restoring force is proportional to displacement and opposite in direction ($ F = -kx $). When plotted, this yields a straight line through the origin with a negative slope.

Question 3

A particle in SHM has $ a = -25 x $ (in SI units). What is its period?

Accepted Answer

For SHM, $ a = -\omega^2 x $. Given $ a = -25 x $, $ \omega^2 = 25 \Rightarrow \omega = 5 \, \text{rad/s} $. Period: $ T = \frac{2\pi}{\omega} = \frac{2\pi}{5} \approx 1.256 \, \text{s} $.

NEET Physics: Oscillations — Practice Set 19

Q1. A simple pendulum has a period of \( 1 \, \text{s} \) on Earth (\( g = 9.8 \, \text{m/s}^2 \)). What is its period on the Moon (\( g = 1.63 \, \text{m/s}^2 \))?

Q2. For a motion to be simple harmonic, the restoring force must satisfy which condition when plotted against displacement?

Q3. A particle in SHM has \( a = -25 x \) (in SI units). What is its period?

Q4. A spring of \( k = 450 \, \text{N/m} \) has a \( 1.5 \, \text{kg} \) mass. If \( E = 2.25 \, \text{J} \), what is the amplitude?

Q5. Why does the period of a spring-mass system remain unaffected by changes in gravitational field strength?

Q6. A spring system has \( m = 0.5 \, \text{kg}, k = 200 \, \text{N/m}, A = 8 \, \text{cm} \). What is the potential energy at \( x = 4 \, \text{cm} \)?

Q7. A particle’s x-projection from circular motion is \( x = 8 \cos (\pi t) \) (in m). What is its maximum speed?

Q8. A body oscillates with SHM according to \( x = 4 \cos (2\pi t + \frac{\pi}{6}) \) (in SI units). What is its velocity at \( t = 0.5 \, \text{s} \)? (Take \( \sin \frac{4\pi}{3} = -\frac{\sqrt{3}}{2} \))

Q9. A particle in SHM has \( x = 4 \sin (4t + \frac{\pi}{6}) \) (in m). What is its speed at \( t = 0.25 \, \text{s} \)? (Take \( \cos 60^\circ = 0.5 \))

Q10. A particle in SHM has \( x = 4 \cos (2t - \frac{\pi}{6}) \) (in m). What is its speed at \( t = 0.5 \, \text{s} \)? (Take \( \sin 30^\circ = 0.5 \))