NEET Oscillations — Set 20

Question 1

What is the significance of the phase constant in the displacement equation of SHM?

Accepted Answer

The phase constant ($ \phi $ in $ x = A \cos (\omega t + \phi) $) determines the initial position and velocity, setting the starting point of the oscillation cycle.

Question 2

Which condition ensures that the total mechanical energy in an SHM system remains conserved during the motion?

Accepted Answer

Total mechanical energy (kinetic + potential) is conserved in SHM when no external dissipative forces (e.g., friction) act, allowing energy to transform without loss.

Question 3

A particle in SHM has $ a = -36 x $ (in SI units). What is its frequency?

Accepted Answer

For SHM, $ a = -\omega^2 x $. Given $ a = -36 x $, $ \omega^2 = 36 \Rightarrow \omega = 6 \, \text{rad/s} $. Frequency: $ v = \frac{\omega}{2\pi} = \frac{6}{2 \times 3.14} \approx 0.955 \, \text{Hz} $.

NEET Physics: Oscillations — Practice Set 20

Q1. What is the significance of the phase constant in the displacement equation of SHM?

Q2. Which condition ensures that the total mechanical energy in an SHM system remains conserved during the motion?

Q3. A particle in SHM has \( a = -36 x \) (in SI units). What is its frequency?

Q4. What underlies the periodic nature of SHM when expressed as a superposition of sine and cosine functions?

Q5. A pendulum has \( L = 1.4 \, \text{m}, g = 9.8 \, \text{m/s}^2 \). What is its angular frequency?

Q6. A particle’s motion is \( x = 4 \sin (3t - \frac{\pi}{3}) \) (in m). What is its velocity at \( t = \frac{\pi}{6} \, \text{s} \)? (Take \( \cos 30^\circ = \frac{\sqrt{3}}{2} \))

Q7. A pendulum of length \( 0.36 \, \text{m} \) oscillates with \( g = 9.8 \, \text{m/s}^2 \). What is its frequency?

Q8. A pendulum has \( L = 0.6 \, \text{m}, g = 9.8 \, \text{m/s}^2 \). What is its angular frequency?

Q9. Which of the following periodic motions cannot be classified as oscillatory due to the absence of a fixed equilibrium point?

Q10. A particle in SHM has \( x = 4 \cos (2t + \frac{\pi}{3}) \) (in m). What is its speed at \( t = 0.5 \, \text{s} \)? (Take \( \sin 60^\circ = \frac{\sqrt{3}}{2} \))