Practice MCQs for JEE Physics Oscillations
Access targeted multiple-choice questions for Oscillations designed to align with the latest JEE academic syllabus for JEE Physics. These objective practice sets help students evaluate their conceptual understanding and improve exam readiness.
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Multiple Choice Questions
(a) zero
(b) −1
(c) 1
(d) infinite
Show Answer & Explanation
Answer: (d) infinite
Explanation:
1. With no damping, energy keeps being supplied at the natural frequency.
2. The amplitude grows without limit in the ideal case.
Teacher's Note:
1. No damping gives infinite amplitude.
Assertion (A): The amplitude of a forced vibration can never reach infinity.
Reason (R): The driving frequency cannot be increased beyond a certain limit.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation
Answer: (c) A is true, but R is false.
Explanation:
1. Real systems have damping, which limits the amplitude, so the assertion is true.
2. The driving frequency can be set to any value, so the reason is false.
Teacher's Note:
1. Damping limits the amplitude.
(a) T and A both decrease
(b) T increases and A is constant
(c) T remains the same and A decreases
(d) T decreases and A is constant
Show Answer & Explanation
Answer: (c) T remains the same and A decreases
Explanation:
1. Air resistance removes energy, so the amplitude decays.
2. The period of small oscillations does not depend on amplitude and stays the same.
Teacher's Note:
1. Damping reduces A, not T.
(a) I only
(b) II only
(c) I and II
(d) I, II and III
Show Answer & Explanation
Answer: (c) I and II
Explanation:
1. The amplitude depends on the driving frequency, so I is false.
2. With damping the amplitude at resonance stays finite, so II is false.
3. III is true.
Teacher's Note:
1. Damping limits the amplitude.
(a) \( \frac\pi3 \)
(b) \( \frac\pi4 \)
(c) \( \frac\pi6 \)
(d) \( \frac\pi2 \)
Show Answer & Explanation
Answer: (a) \( \frac\pi3 \)
Explanation:
1. The separation oscillates about X₀ with amplitude 2A sin(φ/2).
2. Setting 2A sin(φ/2) = A gives φ/2 = π/6, so φ = π/3.
Teacher's Note:
1. Superpose the two SHMs.
(a) \( \frac14m\omega^2A^2 \)
(b) \( \frac14m^2\omega A^2 \)
(c) \( \frac12m\omega^2A^2 \)
(d) \( \frac12m^2\omega^2A^2 \)
Show Answer & Explanation
Answer: (c) \( \frac12m\omega^2A^2 \)
Explanation:
1. E = ½kA² and k = mω².
2. So E = ½mω²A².
Teacher's Note:
1. E = ½mω²A².
(a) tuning fork
(b) forced vibration
(c) free vibration
(d) damped vibration
Show Answer & Explanation
Answer: (b) forced vibration
Explanation:
1. Resonance occurs when a system is driven at its natural frequency, so it is a case of forced vibration.
Teacher's Note:
1. Resonance is forced vibration.
(a) 4
(b) 3
(c) 5
(d) 2
Show Answer & Explanation
Answer: (c) 5
Explanation:
1. T ∝ √l, so T₁ : T₂ = 1.2 : 1 = 6 : 5.
2. When the longer pendulum has made 5 vibrations, the shorter has made 6, so they are together again.
Teacher's Note:
1. Find the least common time.
(a) 0.01 s
(b) 10 s
(c) 0.1 s
(d) 100 s
Show Answer & Explanation
Answer: (a) 0.01 s
Explanation:
1. v_max = Aω gives ω = 4.4/0.007 ≈ 628.6 rad/s.
2. T = 2π/ω ≈ 0.01 s.
Teacher's Note:
1. v_max = Aω.
(a) periodic but not simple harmonic
(b) non-periodic
(c) simple harmonic and the time period is independent of the density of the liquid
(d) simple harmonic and the time period is directly proportional to the density of the liquid
Show Answer & Explanation
Answer: (c) simple harmonic and the time period is independent of the density of the liquid
Explanation:
1. The restoring force is proportional to the density and so is the inertia.
2. T = 2π√(h/g) (h is the column length) does not depend on the density.
Teacher's Note:
1. Density cancels out.
(a) quality factor is small
(b) damping force is small
(c) restoring force is small
(d) applied periodic force is small
Show Answer & Explanation
Answer: (b) damping force is small
Explanation:
1. Smaller damping gives a taller and narrower resonance peak.
Teacher's Note:
1. Low damping, sharp resonance.
(a) A
(b) B
(c) A + B
(d) \( \sqrt{A^2+B^2} \)
Show Answer & Explanation
Answer: (b) B
Explanation:
1. The particle oscillates about the mean position x = A.
2. The displacement from the mean position is B sin ωt, so the amplitude is B.
Teacher's Note:
1. Shift of the origin does not change amplitude.
(a) periodic motion
(b) orbital motion
(c) oscillatory motion
(d) rectilinear motion
Show Answer & Explanation
Answer: (c) oscillatory motion
Explanation:
1. A motion that repeats itself in a to-and-fro manner about a mean position is called an oscillatory motion.
Teacher's Note:
1. To-and-fro means oscillatory.
(a) \( \pi \)
(b) \( 0.707\pi \)
(c) zero
(d) \( 0.5\pi \)
Show Answer & Explanation
Answer: (d) \( 0.5\pi \)
Explanation:
1. If x = A sin ωt, then v = Aω cos ωt and a = −Aω² sin ωt.
2. Velocity leads the acceleration by π/2.
Teacher's Note:
1. v and a differ by π/2.
(a) \( \frac{\sqrt2}{5}\ \text{m} \)
(b) \( \frac1{\sqrt3}\ \text{m} \)
(c) \( \frac{5}{\sqrt2}\ \text{m} \)
(d) \( \frac12\ \text{m} \)
Show Answer & Explanation
Answer: (c) \( \frac{5}{\sqrt2}\ \text{m} \)
Explanation:
1. At t = 1, x = 5 cos(2π − π/4) = 5 cos(π/4).
2. = 5/√2 m.
Teacher's Note:
1. Substitute t = 1.
(a) \( \frac{a}{\sqrt2} \)
(b) \( \frac a2 \)
(c) \( \frac a4 \)
(d) \( a \)
Show Answer & Explanation
Answer: (a) \( \frac{a}{\sqrt2} \)
Explanation:
1. ½k(a² − x²) = ½kx² gives x² = a²/2.
2. So x = a/√2.
Teacher's Note:
1. KE = PE at a/√2.
(a) 0
(b) \( 2\pi/3 \)
(c) \( \pi \)
(d) \( \pi/6 \)
Show Answer & Explanation
Answer: (b) \( 2\pi/3 \)
Explanation:
1. At displacement A/2 moving in opposite directions, the phases are π/6 and π − π/6 = 5π/6.
2. The difference is 5π/6 − π/6 = 2π/3.
Teacher's Note:
1. Opposite velocities, same displacement.
(a) \( \frac{20}{2\pi}\ \text{Hz} \)
(b) \( \frac{10}{2\pi}\ \text{Hz} \)
(c) \( \frac{\pi}{20}\ \text{Hz} \)
(d) \( 2\pi\ \text{Hz} \)
Show Answer & Explanation
Answer: (a) \( \frac{20}{2\pi}\ \text{Hz} \)
Explanation:
1. Comparing with y = a sin(ωt + φ) gives ω = 20 rad/s.
2. f = ω/2π = 20/2π Hz.
Teacher's Note:
1. f = ω/2π.
(a) directly proportional to the displacement
(b) inversely proportional to the displacement
(c) directly proportional to the square of the displacement
(d) inversely proportional to the square of the displacement
Show Answer & Explanation
Answer: (a) directly proportional to the displacement
Explanation:
1. In SHM the restoring force is F = −kx.
2. It is directly proportional to the displacement.
Teacher's Note:
1. F ∝ −x.
Assertion (A): In SHM, kinetic and potential energies become equal when the displacement is 1/√2 times the amplitude.
Reason (R): In SHM, kinetic energy is zero when the potential energy is maximum.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation
Answer: (b) Both A and R are true, but R is not the correct explanation of A.
Explanation:
1. KE = PE at x = A/√2, so the assertion is true.
2. The reason is also true but it does not give the condition for equality.
Teacher's Note:
1. KE = PE at A/√2.
(a) I only
(b) II only
(c) I and II
(d) none of these
Show Answer & Explanation
Answer: (d) none of these
Explanation:
1. Both the elastic properties and the dimensions of a body determine its natural frequency.
2. So neither statement is false.
Teacher's Note:
1. Both statements are true.
Assertion (A): Sine and cosine functions are periodic functions.
Reason (R): Sinusoidal functions repeat their values after a definite interval of time.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation
Answer: (a) Both A and R are true, and R is the correct explanation of A.
Explanation:
1. Sine and cosine repeat after 2π.
2. The reason states exactly this property.
Teacher's Note:
1. Periodic means repeating.
(a) \( \sqrt{\frac{2E}{m}} \)
(b) \( \sqrt{2mE} \)
(c) \( 2mE \)
(d) \( mE^2 \)
Show Answer & Explanation
Answer: (b) \( \sqrt{2mE} \)
Explanation:
1. At the mean position the energy is all kinetic: E = p²/2m.
2. So p = √(2mE).
Teacher's Note:
1. E = p²/2m.
(a) double
(b) four times
(c) half
(d) equal
Show Answer & Explanation
Answer: (a) double
Explanation:
1. KE and PE depend on sin² or cos² of ωt, which have period T/2.
2. Their frequency is double that of the SHM.
Teacher's Note:
1. Energy repeats twice per cycle.
Assertion (A): If the amplitude of a simple pendulum increases, the motion of the pendulum is oscillatory but not simple harmonic.
Reason (R): For larger amplitude θ is large and then sin θ ≠ θ, so the motion is no longer SHM.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation
Answer: (a) Both A and R are true, and R is the correct explanation of A.
Explanation:
1. The restoring torque is proportional to sin θ, not θ.
2. For large θ the motion is not SHM, as the reason states.
Teacher's Note:
1. SHM needs sin θ ≈ θ.
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FAQs
You can get most exhaustive JEE Physics Oscillations MCQs Set 24 for free on StudiesToday.com. These MCQs for JEE Physics are updated for the 2026-27 academic session as per JEE examination standards.
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