Oscillations — Class 11 MCQs with Answers

Oscillations — important questions & MCQs with answers (Class 11 Physics)

6 solved questions from this chapter's difficulty levels, each with its answer and explanation. Tap an option to check yourself.

0 of 6 answered

1. Q1 of 6Easy

   In SHM, restoring force is proportional to:

   AVelocityBDisplacementCAcceleration squaredDMass
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   Answer: Displacement

   Explanation: Newton's SHM law states F = −kx: restoring force is proportional to displacement and directed opposite to it, unlike a velocity-proportional damping force which is the tempting but wrong distractor here.

2. Q2 of 6Easy

   Period of spring-mass system: T = ?

   A2π√(k/m)B2π√(m/k)C2π·m·kDVariable
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   Answer: 2π√(m/k)

   Explanation: For a spring-mass oscillator, T = 2π√(m/k): a larger mass m increases the period while a stiffer spring (larger k) decreases it — inverting the ratio to √(k/m) reverses both trends.

3. Q3 of 6Medium

   Simple pendulum of length 1 m on Earth (g = 9.8):

   A1 sB≈ 2.0 sC4 sDCannot compute
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   Answer: ≈ 2.0 s

   Explanation: Period is T = 2π√(L/g) = 2π√(1 m / 9.8 m/s²) ≈ 2π(0.319) ≈ 2.007 s — using g = 10 m/s² instead of the stated 9.8 shifts the answer slightly, so match g to what the question gives.

4. Q4 of 6Medium

   Amplitude in damped oscillation: A(t) = ?

   AVariableBA₀CConstantDA₀ e^(−γt/2)
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   Answer: A₀ e^(−γt/2)

   Explanation: Damping removes energy in proportion to the current amplitude, giving exponential decay A(t) = A₀e^(−γt/2) — treating A as staying at its initial value A₀ ignores this ongoing energy loss entirely.

5. Q5 of 6Hard

   At resonance, amplitude is limited by:

   AMassBDampingCFrequencyDNothing
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   Answer: Damping

   Explanation: Without damping, driving a system exactly at its natural, resonant frequency would pump in energy every cycle with nothing removing it, so amplitude would grow without bound — damping is what caps how large it can actually get.

6. Q6 of 6Hard

   If x = A sin(ωt), then velocity v =

   A−A sin(ωt)BAω cos(ωt)CAω² sin(ωt)D0
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   Answer: Aω cos(ωt)

   Explanation: Differentiating x = A sin(ωt) gives v = dx/dt = Aω cos(ωt) — velocity leads displacement by 90°. Forgetting the ω factor, as in plain −A sin(ωt), is the tempting but dimensionally wrong distractor.

Oscillations notes: key concepts (Class 11 Physics)

Simple harmonic motion and everything built on it: the defining force law, the displacement, velocity and acceleration equations and their phase relations, SHM as the projection of uniform circular motion, the spring-mass system and simple pendulum, the energy exchange within an oscillation, and damped, forced and resonant oscillations.

Periodic and oscillatory motion

Periodic motion repeats at regular intervals; oscillatory motion is periodic motion to and fro about a fixed equilibrium position.

Simple harmonic motion

Oscillation in which the restoring force is directly proportional to the displacement and always directed towards the mean position.

Displacement in SHM

A sinusoidal function of time, x = A sin(ωt + φ), where A is the amplitude and φ the initial phase fixing the starting point.

Velocity in SHM

Maximum at the mean position and zero at the extremes, and always a quarter cycle ahead of displacement in phase.

Acceleration in SHM

Proportional to displacement but oppositely directed, a = −ω²x. It is zero at the mean position and maximum at the extremes — exactly opposite to velocity.

Phase and phase constant

The phase (ωt + φ) fixes the state of the oscillator at any instant, while the phase constant φ records where in the cycle the motion began.

Angular frequency and period

ω is 2π times the frequency, and the time period T is 2π/ω. For SHM the period is independent of amplitude, which is what makes it useful for clocks.

SHM and circular motion

SHM is the projection of uniform circular motion onto a diameter — the geometric picture behind every sinusoidal formula in the chapter.

Force law for SHM

F = −kx, with the angular frequency √(k/m). Any system whose restoring force takes this form will oscillate harmonically.

Spring-mass system

Its period depends on mass and spring constant only, and notably NOT on g — so it keeps the same period on the Moon as on Earth.

Combination of springs

Springs in parallel add their spring constants; springs in series add their reciprocals, so a series combination is always softer than either alone.

Simple pendulum

Executes SHM only for SMALL angular displacements, where sin θ ≈ θ. Its period depends on length and g but not on the bob's mass.

Energy in SHM

Kinetic and potential energy each oscillate at twice the frequency of the motion, while their sum stays constant at ½kA² throughout.

Damped oscillations

Amplitude decays exponentially because a resistive force removes energy. The frequency shifts slightly below the natural frequency.

Forced oscillations and resonance

A system driven by an external periodic force eventually oscillates at the DRIVING frequency; when that matches the natural frequency the amplitude peaks sharply at resonance.