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1. Motion that repeats itself after equal intervals of time is called
A. Periodic motion
B. Random motion
C. Rectilinear motion
D. Non-uniform motion
Answer: A. Periodic motion
Explanation: Periodic motion is motion that repeats itself identically after a fixed interval of time called the period.
2. Oscillatory motion is periodic motion that occurs
A. To and fro about a mean (equilibrium) position
B. In a straight line without repetition
C. Only in circular paths
D. Only in one direction
Answer: A. To and fro about a mean (equilibrium) position
Explanation: Oscillatory motion is a type of periodic motion in which a body moves back and forth repeatedly about a fixed mean position.
3. The time taken to complete one full oscillation is called
A. Time period
B. Frequency
C. Amplitude
D. Phase
Answer: A. Time period
Explanation: The time period (T) is the time required to complete one full cycle of oscillation.
4. The number of oscillations completed per unit time is called
A. Frequency
B. Time period
C. Amplitude
D. Angular displacement
Answer: A. Frequency
Explanation: Frequency (f) is defined as the number of complete oscillations per unit time, and is the reciprocal of the time period, f = 1/T.
5. The SI unit of frequency is
A. Hertz
B. Second
C. Radian
D. Metre
Answer: A. Hertz
Explanation: The SI unit of frequency is hertz (Hz), equal to one oscillation per second.
6. The maximum displacement of an oscillating particle from its mean position is called
A. Amplitude
B. Phase
C. Frequency
D. Angular velocity
Answer: A. Amplitude
Explanation: Amplitude is defined as the maximum displacement of an oscillating body from its mean (equilibrium) position.
7. Simple harmonic motion (SHM) is defined as oscillatory motion in which the restoring force is
A. Directly proportional to displacement and directed towards the mean position
B. Constant in magnitude and direction
C. Inversely proportional to displacement
D. Directed away from the mean position
Answer: A. Directly proportional to displacement and directed towards the mean position
Explanation: In SHM, the restoring force F = -kx is proportional to the displacement x and always directed towards the mean (equilibrium) position.
8. The negative sign in the SHM force equation F = -kx indicates that the force is
A. Always directed opposite to the displacement
B. Always in the same direction as displacement
C. Zero at all times
D. Independent of displacement
Answer: A. Always directed opposite to the displacement
Explanation: The negative sign shows that the restoring force always acts opposite to the displacement, pulling the particle back toward the mean position.
9. The time period of a simple pendulum depends on
A. Its length and the acceleration due to gravity
B. The mass of the bob only
C. The amplitude of oscillation only
D. The material of the bob
Answer: A. Its length and the acceleration due to gravity
Explanation: The time period of a simple pendulum is given by T = 2π√(L/g), depending only on its length L and the local acceleration due to gravity g (for small oscillations).
10. If the length of a simple pendulum is quadrupled, its time period becomes
A. Double
B. Half
C. Four times
D. Unchanged
Answer: A. Double
Explanation: Since T ∝ √L, quadrupling the length increases the time period by a factor of √4 = 2, so the time period doubles.
11. The time period of a mass-spring system executing SHM is given by
A. T = 2π√(m/k)
B. T = 2π√(k/m)
C. T = 2π(m/k)
D. T = 2πmk
Answer: A. T = 2π√(m/k)
Explanation: For a mass m attached to a spring of force constant k undergoing SHM, the time period is T = 2π√(m/k).
12. In SHM, the velocity of the particle is maximum at
A. The mean position
B. The extreme positions
C. Both mean and extreme positions equally
D. Nowhere; velocity is always constant
Answer: A. The mean position
Explanation: In SHM, velocity is maximum at the mean position (where displacement is zero) and decreases to zero at the extreme positions.
13. In SHM, the acceleration of the particle is maximum at
A. The extreme positions
B. The mean position
C. Both mean and extreme positions equally
D. Nowhere; acceleration is always zero
Answer: A. The extreme positions
Explanation: Since acceleration in SHM is a = -ω²x, it is maximum in magnitude at the extreme positions where displacement x is maximum.
14. In SHM, the total mechanical energy of the oscillating system is
A. Constant at all positions during oscillation
B. Maximum at the mean position only
C. Maximum at the extreme positions only
D. Zero throughout the motion
Answer: A. Constant at all positions during oscillation
Explanation: In SHM (ignoring damping), the total mechanical energy (kinetic + potential) remains constant, though it continuously interconverts between kinetic and potential forms.
15. At the mean position in SHM, the kinetic energy is
A. Maximum, and potential energy is minimum
B. Minimum, and potential energy is maximum
C. Both zero
D. Both maximum
Answer: A. Maximum, and potential energy is minimum
Explanation: At the mean position, velocity is maximum so kinetic energy is maximum, while displacement is zero, making potential energy minimum (often taken as zero).
16. Damped oscillations occur when a system experiences
A. A resistive force that gradually reduces the amplitude over time
B. A force that increases amplitude continuously
C. No external force at all
D. Only a restoring force with no friction
Answer: A. A resistive force that gradually reduces the amplitude over time
Explanation: Damped oscillations occur when a dissipative force, such as friction or air resistance, causes the amplitude of oscillation to decrease gradually with time.
17. Forced oscillations occur when a system oscillates under the influence of
A. A periodic external force
B. Its own natural frequency alone with no external influence
C. Gravity only
D. A constant, non-periodic force
Answer: A. A periodic external force
Explanation: Forced oscillations occur when an external periodic force continuously drives a system, causing it to oscillate at the frequency of the applied force.
18. Resonance occurs when the frequency of the external driving force
A. Matches the natural frequency of the system, causing a large increase in amplitude
B. Is much greater than the natural frequency
C. Is zero
D. Has no relation to amplitude
Answer: A. Matches the natural frequency of the system, causing a large increase in amplitude
Explanation: Resonance occurs when the driving frequency equals the natural frequency of the system, resulting in a dramatic increase in the amplitude of oscillation.
19. Why did the Tacoma Narrows Bridge collapse historically become a well-known example in physics?
A. It illustrated the destructive effect of resonance from wind-induced oscillations
B. It was destroyed due to an earthquake unrelated to oscillations
C. It demonstrated perfectly damped motion
D. It had no connection to periodic motion
Answer: A. It illustrated the destructive effect of resonance from wind-induced oscillations
Explanation: The bridge's collapse is often cited as an example of how oscillations driven near a structure's natural frequency can build up to dangerously large amplitudes, referencing the concept of resonance.
20. The phase constant (or phase angle) in the SHM equation x = A sin(ωt + φ) represents
A. The initial state (position/direction) of the oscillating particle at t = 0
B. The amplitude of oscillation
C. The angular frequency
D. The time period of motion
Answer: A. The initial state (position/direction) of the oscillating particle at t = 0
Explanation: The phase constant φ determines the state of motion (initial displacement and direction) of the oscillating particle at the starting time t = 0.
21. The relationship between angular frequency ω and time period T is
A. ω = 2π/T
B. ω = T/2π
C. ω = 2πT
D. ω = π/T
Answer: A. ω = 2π/T
Explanation: Angular frequency is related to the time period by ω = 2π/T = 2πf, where f is the frequency.
22. Uniform circular motion, when projected onto a diameter, produces
A. Simple harmonic motion
B. Uniformly accelerated linear motion
C. Random motion
D. Constant velocity motion
Answer: A. Simple harmonic motion
Explanation: The projection of a particle moving in uniform circular motion onto any diameter of the circle executes simple harmonic motion.
23. A child on a swing continues to swing (with decreasing height) after being given one push mainly because of
A. Damping due to air resistance and friction gradually reducing energy
B. Continuous external force acting throughout
C. Resonance with the wind
D. Increasing potential energy over time
Answer: A. Damping due to air resistance and friction gradually reducing energy
Explanation: Without repeated pushes, a swing's oscillation amplitude gradually decreases due to dissipative forces like air resistance and friction at the pivot, an example of damped oscillation.
24. If the amplitude of SHM is doubled, the total energy of the oscillator becomes
A. Four times
B. Double
C. Half
D. Unchanged
Answer: A. Four times
Explanation: Since total energy in SHM is proportional to the square of the amplitude (E ∝ A²), doubling the amplitude increases the energy four-fold.
25. The time period of a simple pendulum on the Moon, compared to Earth, would be
A. Longer, since gravity on the Moon is weaker
B. Shorter, since gravity on the Moon is weaker
C. The same as on Earth
D. Zero, since there is no gravity on the Moon
Answer: A. Longer, since gravity on the Moon is weaker
Explanation: Since T = 2π√(L/g) and g on the Moon is about one-sixth that of Earth, a pendulum would swing more slowly, giving a longer time period on the Moon.
26. All simple harmonic motions are periodic, but all periodic motions
A. Need not be simple harmonic
B. Must always be simple harmonic
C. Cannot exist without SHM
D. Are identical to circular motion
Answer: A. Need not be simple harmonic
Explanation: While every SHM is periodic, not every periodic motion satisfies the specific condition of a restoring force proportional to displacement, so not all periodic motion is SHM.
27. For small angular displacements, the motion of a simple pendulum approximates SHM because
A. sin θ ≈ θ (in radians) for small angles, making the restoring force proportional to displacement
B. Gravity becomes zero for small angles
C. The pendulum stops moving for small angles
D. Tension in the string becomes infinite
Answer: A. sin θ ≈ θ (in radians) for small angles, making the restoring force proportional to displacement
Explanation: For small angular displacements, the approximation sin θ ≈ θ allows the restoring force on the pendulum bob to become directly proportional to displacement, satisfying the condition for SHM.
28. In SHM, displacement and acceleration are related such that acceleration is always
A. Directed opposite to displacement and proportional to it
B. In the same direction as displacement
C. Independent of displacement
D. Constant throughout the motion
Answer: A. Directed opposite to displacement and proportional to it
Explanation: In SHM, a = -ω²x, meaning acceleration is always directly proportional to displacement but points in the opposite direction, toward the mean position.
29. Vibrations of a tuning fork after being struck are an example of
A. Damped oscillations
B. Undamped, non-decaying oscillations
C. Forced oscillations only
D. Non-periodic motion
Answer: A. Damped oscillations
Explanation: A struck tuning fork vibrates with gradually decreasing amplitude due to resistive forces like air friction, making it an example of damped oscillation.
30. If a pendulum clock is taken to a place of higher altitude (where g decreases slightly), the clock will
A. Run slower, since its time period increases
B. Run faster, since its time period decreases
C. Show no change at all
D. Stop working completely
Answer: A. Run slower, since its time period increases
Explanation: Since T = 2π√(L/g), a decrease in g at higher altitude increases the pendulum's time period, causing the clock to tick more slowly and thus run slower.
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