1. What is the period of a motion?

A) The time taken for the object to travel a fixed distance
B) The time taken for one complete oscillation or cycle
C) The smallest distance between two points of motion
D) The time taken to return to the mean position

Answer: B) The time taken for one complete oscillation or cycle

2. Which of the following is a property of simple harmonic motion (SHM)?

A) The motion is non-repetitive
B) Displacement varies as a linear function of time
C) The restoring force is proportional to displacement and directed towards the mean position
D) The frequency changes with time

Answer: C) The restoring force is proportional to displacement and directed towards the mean position

3. Which of the following equations describes simple harmonic motion (SHM)?

A) $x(t) = A \sin(\omega t + \phi)$
B) $x(t) = A e^{-\omega t}$
C) $x(t) = A \ln(\omega t)$
D) $x(t) = A t^2$

Answer: A) $x(t) = A \sin(\omega t + \phi)$

4. What is the relationship between frequency ( $\nu$ ) and period ( $T$ )?

A) $\nu = T$
B) $\nu = 1/T$
C) $\nu = T^2$
D) $\nu = 1/T^2$

Answer: B) $\nu = 1/T$

5. Which of the following motions is always periodic but not necessarily oscillatory?

A) The swing of a pendulum
B) The orbital motion of planets
C) The oscillation of a spring-mass system
D) The vibration of a guitar string

Answer: B) The orbital motion of planets

6. What happens to the acceleration of a particle in SHM when its displacement increases?

A) Acceleration becomes zero
B) Acceleration increases and is directed away from the mean position
C) Acceleration decreases
D) Acceleration increases and is directed towards the mean position

Answer: D) Acceleration increases and is directed towards the mean position

7. In SHM, what is the energy of the system at the mean position?

A) Entirely kinetic energy
B) Entirely potential energy
C) Zero
D) Equally divided between kinetic and potential energy

Answer: A) Entirely kinetic energy

8. A simple pendulum exhibits SHM if:

A) The displacement is very large
B) The string is not rigid
C) The angular displacement is small
D) The pendulum is released with a horizontal velocity

Answer: C) The angular displacement is small

9. What is the angular frequency ( $\omega$ ) in SHM if the time period is $T$ ?

A) $\omega = 1/T$
B) $\omega = T/2\pi$
C) $\omega = 2\pi/T$
D) $\omega = T^2$

Answer: C) $\omega = 2\pi/T$

10. In SHM, which statement about kinetic energy ( $K$ ) and potential energy ( $U$ ) is true?

A) $K$ and $U$ are always equal
B) $K$ and $U$ vary periodically and their sum remains constant
C) $K$ remains constant while $U$ changes periodically
D) $K$ increases with time while $U$ decreases

Answer: B) $K$ and $U$ vary periodically and their sum remains constant

11. Which of the following quantities remain constant during SHM?

A) Displacement
B) Velocity
C) Acceleration
D) Total mechanical energy

Answer: D) Total mechanical energy

12. Which of the following is an example of periodic but not simple harmonic motion?

A) Motion of a pendulum at small angles
B) Oscillations of a spring-mass system
C) The rotation of the Earth about its axis
D) Vibrations of a tuning fork

Answer: C) The rotation of the Earth about its axis

13. What happens to the period of a simple pendulum if its length is quadrupled?

A) The period doubles
B) The period becomes half
C) The period remains the same
D) The period quadruples

Answer: A) The period doubles

14. What is the relationship between the maximum velocity ( $v_m$ ) and angular frequency ( $\omega$ ) in SHM?

A) $v_m = A/\omega$
B) $v_m = \omega A$
C) $v_m = \omega^2 A$
D) $v_m = \omega^3 A$

Answer: B) $v_m = \omega A$

15. What is the restoring force for a mass $m$ attached to a spring of constant $k$ ?

A) $F = -kx^2$
B) $F = -kx$
C) $F = -kx/m$
D) $F = kx$

Answer: B) $F = -kx$

16. Which of the following correctly defines the angular frequency $\omega$ in terms of the spring constant $k$ and mass $m$ ?

A) $\omega = \sqrt{k/m}$
B) $\omega = \sqrt{m/k}$
C) $\omega = k/m$
D) $\omega = m/k$

Answer: A) $\omega = \sqrt{k/m}$

17. What type of force leads to simple harmonic motion?

A) Constant force
B) Inverse-square law force
C) Force proportional to displacement and directed towards equilibrium
D) Frictional force

Answer: C) Force proportional to displacement and directed towards equilibrium

18. The time period of a simple pendulum depends on:

A) Mass of the bob
B) Amplitude of oscillation
C) Length of the string
D) Both mass and length

Answer: C) Length of the string

19. Which term describes the maximum displacement of a particle in SHM from its equilibrium position?

A) Amplitude
B) Frequency
C) Period
D) Phase

Answer: A) Amplitude

20. In SHM, when the particle is at maximum displacement:

A) Velocity is maximum
B) Acceleration is zero
C) Kinetic energy is maximum
D) Acceleration is maximum

Answer: D) Acceleration is maximum

21. What is the phase constant ( $\phi$ ) in SHM?

A) A measure of the total energy in the motion
B) The initial angular position at $t = 0$
C) The maximum displacement of the particle
D) The rate of change of displacement with time

Answer: B) The initial angular position at $t = 0$

22. The displacement in SHM is expressed as $x(t) = A \cos(\omega t + \phi)$ . What does $\phi$ determine?

A) The frequency of the motion
B) The starting position of the motion
C) The total energy of the system
D) The period of oscillation

Answer: B) The starting position of the motion

23. For a mass-spring system executing SHM, the potential energy is maximum when:

A) The displacement is zero
B) The velocity is maximum
C) The displacement is maximum
D) The acceleration is zero

Answer: C) The displacement is maximum

24. Which of the following is true for kinetic and potential energy in SHM?

A) Both energies reach their maximum at the same time
B) Both energies are zero at the mean position
C) Kinetic energy is maximum at the mean position
D) Potential energy is constant throughout

Answer: C) Kinetic energy is maximum at the mean position

25. If the frequency of SHM is doubled, what happens to the angular frequency ( $\omega$ )?

A) It is halved
B) It remains unchanged
C) It is doubled
D) It becomes four times

Answer: C) It is doubled

26. Which of the following graphs represents displacement in SHM?

A) A parabolic curve
B) A sine or cosine curve
C) A straight line with a positive slope
D) An exponential curve

Answer: B) A sine or cosine curve

27. What type of motion is performed by the projection of uniform circular motion on the diameter of the circle?

A) Circular motion
B) Random motion
C) Simple harmonic motion
D) Projectile motion

Answer: C) Simple harmonic motion

28. In a simple pendulum, the restoring force depends on:

A) The length of the pendulum
B) The mass of the bob
C) The angular displacement
D) Both mass and length

Answer: C) The angular displacement

29. The total energy of a particle in SHM depends on:

A) Its displacement from the equilibrium position
B) Its velocity at a given time
C) The amplitude of motion
D) The phase constant

Answer: C) The amplitude of motion

30. The angular frequency of a simple pendulum is related to its length $L$ by:

A) $\omega = \sqrt{L/g}$
B) $\omega = \sqrt{g/L}$
C) $\omega = g/L$
D) $\omega = L/g$

Answer: B) $\omega = \sqrt{g/L}$

31. What is the condition for a motion to be classified as simple harmonic motion (SHM)?

A) The displacement must be a constant
B) The restoring force must vary linearly with displacement
C) The frequency must change over time
D) The motion must follow a quadratic function

Answer: B) The restoring force must vary linearly with displacement

32. In SHM, the phase difference between displacement and acceleration is:

A) $0$
B) $\pi/2$
C) $\pi$
D) $2\pi$

Answer: C) $\pi$

33. Which of the following represents the potential energy ( $U$ ) of a particle in SHM?

A) $U = \frac{1}{2} m v^2$
B) $U = \frac{1}{2} k A^2$
C) $U = \frac{1}{2} k x^2$
D) $U = m \omega^2 A^2$

Answer: C) $U = \frac{1}{2} k x^2$

34. The frequency of oscillation for a simple pendulum depends on:

A) Length of the pendulum and the amplitude of oscillation
B) Acceleration due to gravity and length of the pendulum
C) Mass of the bob and the angular displacement
D) Acceleration due to gravity and the mass of the bob

Answer: B) Acceleration due to gravity and length of the pendulum

35. The velocity of a particle in SHM is maximum when the:

A) Displacement is maximum
B) Acceleration is maximum
C) Displacement is zero
D) Potential energy is maximum

Answer: C) Displacement is zero

36. Which of the following describes the motion of a simple pendulum at small angular displacements?

A) Non-periodic
B) Periodic but not simple harmonic
C) Simple harmonic motion
D) Uniform circular motion

Answer: C) Simple harmonic motion

37. A mass-spring system oscillates with an amplitude of $A$ . At what displacement is the kinetic energy equal to the potential energy?

A) $x = 0$
B) $x = A/2$
C) $x = \sqrt{A/2}$
D) $x = A/\sqrt{2}$

Answer: D) $x = A/\sqrt{2}$

38. Which of the following is true about SHM?

A) The period depends on the amplitude
B) The total energy increases with time
C) The restoring force always points towards the equilibrium position
D) The displacement and velocity are in phase

Answer: C) The restoring force always points towards the equilibrium position

39. In SHM, the displacement of a particle is described by $x(t) = A \cos(\omega t)$ . What is the velocity of the particle at $t = T/4$ , where $T$ is the period?

A) $\omega A$
B) $0$
C) $-\omega A$
D) $\omega A/\sqrt{2}$

Answer: D) $\omega A/\sqrt{2}$

40. In the equation $x(t) = A \cos(\omega t + \phi)$ , what is the meaning of $\omega$ ?

A) It is the time period of the motion
B) It is the angular displacement of the particle
C) It is the angular frequency of the motion
D) It is the amplitude of the motion

Answer: C) It is the angular frequency of the motion

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Thursday, November 21, 2024

MCQ Physics Chapter–14: Oscillations, HS 1st year