Oscillations — 50 High-Yield MCQs (NCERT / NEET)

Covers simple harmonic motion, period & frequency, energy in oscillators, damped & forced oscillations, resonance, pendulums, torsional oscillators and key formulas. Correct answers shown after each question.

50 MCQs
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SHM Basics Energy & Phase Damping & Resonance Pendulum & Torsion
1. Simple harmonic motion (SHM) is characterized by acceleration proportional to:
A. Displacement (a ∝ +x)
B. Negative displacement (a ∝ −x)
C. Velocity
D. Time
Answer: B
2. Equation of motion for SHM is ẍ + ω^2 x = 0. ω here is:
A. Angular frequency
B. Linear frequency
C. Period
D. Phase
Answer: A
3. For a mass-spring system, angular frequency ω equals:
A. √(m/k)
B. √(k/m)
C. 2π√(m/k)
D. k/m
Answer: B
4. Period T of SHM is related to ω by:
A. T = ω
B. T = 2π/ω
C. T = ω/2π
D. T = 1/ω^2
Answer: B
5. Frequency f is reciprocal of period. f equals:
A. f = ω × 2π
B. f = 1/T
C. f = T
D. f = ω^2
Answer: B
6. Displacement in SHM can be written as x(t) = A cos(ωt + φ). φ is called:
A. Amplitude
B. Phase constant
C. Frequency
D. Damping factor
Answer: B
7. Maximum velocity in SHM with amplitude A is:
A. A ω
B. A / ω
C. ω / A
D. A ω^2
Answer: A
8. Maximum acceleration in SHM with amplitude A is:
A. A ω
B. A ω^2
C. ω^2 / A
D. A/ω
Answer: B
9. Total energy in a mass-spring SHM with mass m and spring constant k is:
A. (1/2) k A^2
B. (1/2) m v^2 only
C. k A
D. m g A
Answer: A
10. In SHM energy oscillates between:
A. Kinetic and potential energy
B. Thermal and chemical energy
C. Electrical and magnetic energy
D. Mass and energy
Answer: A
11. Phase difference between displacement and velocity in SHM is:
A. 0
B. π/2 (90°)
C. π (180°)
D. 2π
Answer: B
12. Small-angle approximation sinθ ≈ θ (in radians) is used to derive SHM for:
A. Simple pendulum
B. Mass-spring only
C. Torsional pendulum only
D. Damped oscillator only
Answer: A
13. Period of a simple pendulum for small oscillations is T = 2π √(l/g). T is independent of:
A. Length l
B. Mass of bob
C. Gravity g
D. Amplitude (small)
Answer: B
14. For torsional pendulum with torsion constant κ and moment of inertia I, angular frequency ω is:
A. √(I/κ)
B. √(κ/I)
C. κ/I
D. I/κ
Answer: B
15. Damped oscillation becomes overdamped when damping constant b satisfies:
A. b^2 < 4 m k
B. b^2 = 4 m k
C. b^2 > 4 m k
D. b = 0
Answer: C
16. Critical damping occurs when:
A. b^2 < 4 m k
B. b^2 = 4 m k
C. b^2 > 4 m k
D. b = 0
Answer: B
17. In underdamped motion the amplitude decays approximately as:
A. Exponential (A e^{−γ t})
B. Linear
C. Quadratic
D. Constant
Answer: A
18. Quality factor Q of an oscillator is defined as Q =:
A. ω0 / (2β) where β is damping coefficient
B. 2β / ω0
C. ω0 × β
D. 1/ω0
Answer: A
19. Resonance occurs when a driven oscillator is forced at frequency close to:
A. Zero frequency
B. Natural frequency
C. Twice natural frequency
D. Any frequency
Answer: B
20. In forced oscillations with damping, steady-state amplitude is maximum near:
A. Natural frequency (shifted by damping)
B. Zero
C. Infinity
D. Twice frequency
Answer: A
21. Phase lag between driving force and displacement at resonance (for lightly damped oscillator) is approximately:
A. 0
B. π/2
C. π
D. −π/2
Answer: B
22. For small oscillations of a physical pendulum, period T = 2π √(I/mgh), where I is moment of inertia about pivot and h is:
A. Distance from pivot to center of mass
B. Mass
C. Gravity
D. Angular frequency
Answer: A
23. In SHM, average kinetic energy over one cycle equals average potential energy and equals:
A. Total energy
B. Half of total energy
C. Zero
D. Twice total energy
Answer: B
24. Beat frequency between two oscillations of frequencies f1 and f2 is:
A. f1 + f2
B. |f1 − f2|
C. f1 × f2
D. f1 / f2
Answer: B
25. For a mass-spring system, potential energy at displacement x is:
A. k x
B. (1/2) k x^2
C. k x^2
D. (1/2) m v^2
Answer: B
26. For small torsional oscillations, restoring torque τ is proportional to angular displacement θ as τ = −C θ. C is called:
A. Torsion constant
B. Damping constant
C. Moment of inertia
D. Angular momentum
Answer: A
27. In SHM amplitude A depends on initial conditions. For small damping, A of free oscillation:
A. Remains constant
B. Decreases with time
C. Increases with time
D. Oscillates irregularly
Answer: B
28. In a driven damped oscillator at steady state, transient solutions die out due to:
A. Resonance
B. Damping
C. Driving only
D. No damping
Answer: B
29. The amplitude response curve width at half maximum is inversely related to:
A. Damping
B. Quality factor Q
C. Mass only
D. Spring constant only
Answer: B
30. For a mass-spring system oscillating vertically, equilibrium is shifted by gravity but period remains approximately:
A. Dependent on amplitude
B. T = 2π√(m/k) (same as horizontal case)
C. Infinity
D. Zero
Answer: B
31. When two oscillators of nearly equal frequency are weakly coupled, energy is exchanged periodically producing:
A. Damping
B. Beats (modulation)
C. Chaos
D. No motion
Answer: B
32. Small oscillations about stable equilibrium in potential V(x) occur with frequency determined by:
A. V''(x0)/m (second derivative at equilibrium)
B. V(x0) only
C. First derivative V'(x0)
D. Mass only
Answer: A
33. For SHM the displacement, velocity and acceleration are all sinusoidal but acceleration leads displacement by phase:
A. 0
B. π/2
C. π
D. 3π/2
Answer: C
34. In an undriven damped oscillator mechanical energy decays due to:
A. Conversion to potential energy
B. Dissipation as heat (friction)
C. Increase of amplitude
D. External work input
Answer: B
35. If damping is very small, the damped angular frequency ω_d equals approximately:
A. ω0
B. ω0 √(1 − (b/2mω0)^2) ≈ ω0
C. 0
D. Infinity
Answer: B
36. For a driven oscillator, in steady state power absorbed by oscillator is maximum near:
A. Low frequency
B. Resonance frequency
C. Zero frequency
D. Twice frequency
Answer: B
37. For a simple pendulum, increasing amplitude (beyond small angles) causes period to:
A. Decrease slightly
B. Increase slightly (nonlinear effect)
C. Remain exactly same
D. Become zero
Answer: B
38. A driven oscillator with low damping shows sharp resonance peak and thus a high:
A. Damping coefficient
B. Quality factor Q
C. Mass
D. Restoring force
Answer: B
39. When two harmonic motions of the same frequency and amplitude are in phase, their superposition gives amplitude equal to:
A. A (same)
B. 2A
C. 0
D. √2 A
Answer: B
40. The mathematical form of damped harmonic motion is x(t) = A e^{−γ t} cos(ω_d t + φ). γ represents:
A. Driving frequency
B. Damping rate (decay constant)
C. Natural frequency
D. Phase
Answer: B
41. In the context of oscillations, 'phase velocity' usually refers to wave motion. For a single harmonic oscillator, phase refers to:
A. Spatial speed
B. Instantaneous angle ωt + φ specifying state
C. Energy
D. Amplitude
Answer: B
42. For small oscillations of a mass at the bottom of a potential well V(x), frequency ω = √(V''(x0)/m). This is obtained by Taylor expanding V(x) to:
A. First order only
B. Second order (quadratic) around minimum
C. Third order
D. Zero order
Answer: B
43. When coupling between oscillators is strong, normal modes have:
A. Same frequency only
B. Distinct normal frequencies and mode shapes
C. No oscillation
D. Infinite frequency
Answer: B
44. For a pendulum clock, isochronism means period is independent of amplitude. Ideal small-angle pendulum approximates isochronism but practical clocks ensure small amplitude to:
A. Increase period
B. Maintain constant period
C. Stop motion
D. Randomize ticks
Answer: B
45. In resonance application, a high Q is desirable for:
A. Wide bandwidth
B. Narrow bandwidth and sharp frequency selectivity
C. Strong damping
D. Low amplitude
Answer: B
46. Phase portrait of simple harmonic oscillator in (x, v) plane is:
A. Straight line
B. Circle/ellipse (closed orbit)
C. Parabola
D. Random scatter
Answer: B
47. If two SHMs of same frequency are out of phase by π, their superposition results in:
A. Constructive interference
B. Destructive interference (cancellation)
C. Beats
D. Resonance
Answer: B
48. Energy dissipated per cycle for a damped oscillator is proportional to:
A. Q
B. 1/Q
C. Q^2
D. Independent of Q
Answer: B
49. The Floquet theorem deals with stability of solutions for:
A. Linear time-invariant systems only
B. Linear differential equations with periodic coefficients (parametric oscillations)
C. Nonlinear algebraic equations
D. Static equilibrium only
Answer: B
50. Mathieu's equation describes behaviour of:
A. Damped harmonic oscillator only
B. Parametrically driven oscillators (stability regions)
C. Simple pendulum only
D. Thermal diffusion
Answer: B