A simple pendulum's amplitude decays exponentially because of air drag and pivot friction. Plot amplitude squared (A²) vs time t — A² ∝ E (mechanical energy). The graph is approximately a decaying exponential; for small damping, slope of ln(A²) vs t gives the energy dissipation rate.
-- NCERT Physics Lab Manual Class 11, Part 9, p. 148Experiment 03 Simple Pendulum Damping
8 MCQs8-step worked example
Source: NCERT Experimental SkillsOfficial key: NTA-verifiedLast updated: 24 Sep 2026
Experiment 03 Simple Pendulum Damping, explained for NEET
The common failure in this experiment is plotting the wrong quantity. Students record amplitude and plot amplitude against time, then talk about "energy falling linearly". The graph this experiment asks for is the square of amplitude against time, because it is the square that tracks energy, not the amplitude itself.
For a pendulum swinging through small angles, the total mechanical energy at any instant is proportional to the square of the amplitude of that swing. Halve the amplitude and you are left with a quarter of the energy, not half. That single proportionality is the whole reason the y-axis carries A² and not A — see the simple-pendulum dissipation experiment in the NCERT Physics Lab Manual Class 11, Part 9, page 148.
The procedure is deliberately plain: set the bob swinging with a small displacement, place a horizontal scale under the mean position, and read off the amplitude after every fixed number of complete oscillations. The oscillation count is the clock — the time period stays effectively constant while the amplitude dies away, so counting swings and multiplying by T gives the time coordinate without a fresh stopwatch reading each time (NCERT Physics Lab Manual Class 11, Part 9, page 149).
The resulting A²-versus-time plot is a falling curve, steep at first and flattening as it approaches the time axis. It is not a straight line. Energy is lost to air drag on the bob and to friction at the point of suspension, and the rate of loss is largest when the swing is largest — a decaying curve is exactly what that produces.
In NEET this experiment appears as a short reasoning or one-step calculation question: what the axes mean, what factor the energy has dropped by, or what the shape of the curve tells you.
Watch out: keep the initial displacement small. Beyond roughly 15°, the motion is no longer simple harmonic and the energy–amplitude-squared relation you are testing no longer applies cleanly.
Can you answer these Experiment 03 Simple Pendulum Damping MCQs?
Select an option to see the explanation. Wrong answers show why your choice was tempting — and name the exact trap it exploits.
MCQ 1Easy RecallPractice
In the simple-pendulum dissipation experiment, the total energy of the oscillating pendulum at any instant is proportional to:
Show answer and why every option is right or wrong
Answer: C. C is correct: the energy of a small-angle pendulum goes as the square of the amplitude, which is why the experiment plots A² and not A on the vertical axis (NCERT Physics Lab Manual Class 11, Part 9, page 148).
Why A is wrong: A is wrong: energy is not linear in amplitude, and taking it as linear is what leads students to plot A against t and then describe the loss as uniform.
Why B is wrong: B is wrong: no square root appears in the energy of a harmonic oscillator; this option inverts the actual power of the amplitude.
Why D is wrong: D is wrong: energy falls as the swing dies away, whereas a reciprocal relation would make energy grow without limit as the amplitude approaches zero.
MCQ 2Easy RecallPractice
In this experiment, the steady loss of the pendulum's energy is caused mainly by:
Show answer and why every option is right or wrong
Answer: A. A is correct: the dissipative agents in this experiment are air drag on the bob and friction at the support, and they are what make the swing decay at all (NCERT Physics Lab Manual Class 11, Part 9, page 149).
Why B is wrong: B is wrong: the weight is the restoring agent, not a dissipative one, and a conservative force cannot drain the total mechanical energy.
Why C is wrong: C is wrong: g is taken as fixed at a given place, and a changing g would alter the time period, which this experiment relies on staying constant.
Why D is wrong: D is wrong: the string is treated as inextensible in the working of this experiment, so stretching is not a loss channel here.
MCQ 3Easy RecallPractice
While the pendulum is swinging, the amplitude of each recorded swing is read using:
Show answer and why every option is right or wrong
Answer: D. D is correct: the amplitude is read directly off a horizontal scale fixed under the bob, with the mean position marked as the origin of that reading (NCERT Physics Lab Manual Class 11, Part 9, page 148).
Why A is wrong: A is wrong: a screw gauge measures a static thickness or diameter of a small object and cannot be applied to a moving bob to give a swing amplitude.
Why B is wrong: B is wrong: a calliper on the thread would measure the thread's own diameter, not the horizontal displacement of the bob.
Why C is wrong: C is wrong: a stopwatch gives the time coordinate, not the amplitude; timing and amplitude are separate readings in this experiment.
MCQ 4Direct ApplicationPractice
The amplitude of a damped pendulum falls from 12.0 cm to 6.0 cm. The energy at the later instant, as a fraction of the energy at the earlier instant, is:
Show answer and why every option is right or wrong
Answer: B. B is correct: energy goes as the square of the amplitude, so halving the amplitude leaves (1/2)² = 1/4 of the energy (NCERT Physics Lab Manual Class 11, Part 9, page 148).
Why A is wrong: A is wrong: it treats energy as proportional to amplitude itself, the exact substitution this experiment is designed to break.
Why C is wrong: C is wrong: it cubes the amplitude ratio, whereas the exponent in the energy relation is two.
Why D is wrong: D is wrong: it takes the square root of the amplitude ratio instead of its square, inverting the power.
MCQ 5Direct ApplicationPractice
On the A²-versus-time graph, a student marks the instant at which the pendulum's energy has dropped to half its starting value. At that instant, the amplitude equals the initial amplitude A₀ multiplied by:
Show answer and why every option is right or wrong
Answer: A. A is correct: half the energy means half of A₀², so the amplitude is A₀/√2, about 0.707 A₀ (NCERT Physics Lab Manual Class 11, Part 9, page 148).
Why B is wrong: B is wrong: an amplitude of A₀/2 corresponds to one quarter of the energy, not one half.
Why C is wrong: C is wrong: A₀/4 leaves one sixteenth of the energy, because this option halves the amplitude twice over.
Why D is wrong: D is wrong: A₀/(2√2) leaves one eighth of the energy, which is three successive halvings of energy rather than one.
MCQ 6Concept TrapPractice
A student plots the square of the amplitude against time for a freely damped pendulum. The plot obtained is:
Show answer and why every option is right or wrong
Answer: D. D is correct: the energy loss per unit time is largest when the swing is largest, so A² falls quickly at first and then more gently, giving a decaying curve rather than a line (NCERT Physics Lab Manual Class 11, Part 9, page 150).
Why A is wrong: A is wrong: it shows energy increasing, and nothing in a freely swinging damped pendulum feeds energy back in.
Why B is wrong: B is wrong: it confuses the constancy of the time period with constancy of the energy; the period stays nearly fixed while the energy falls.
Why C is wrong: C is wrong: a constant negative slope would mean a fixed energy loss per second however small the swing had become, which contradicts the observed flattening.
MCQ 7Direct ApplicationPractice
A pendulum in this experiment has a time period of 2.0 s. Amplitude readings are taken after every 10 complete oscillations (10 is an exact count), with the first reading taken at t = 0. The time coordinate of the fourth reading is:
Show answer and why every option is right or wrong
Answer: C. C is correct: the fourth reading comes after three blocks of 10 oscillations, that is 30 oscillations × 2.0 s = 60.0 s, using the oscillation count as the clock (NCERT Physics Lab Manual Class 11, Part 9, page 149).
Why A is wrong: A is wrong: 20.0 s is the second reading, taken after the first block of 10 oscillations.
Why B is wrong: B is wrong: 40.0 s is the third reading, and this option forgets that the first reading sits at t = 0, so the number of blocks is one less than the reading number.
Why D is wrong: D is wrong: 80.0 s corresponds to 40 oscillations, which would be the fifth reading.
MCQ 8CalculationPractice
A damped pendulum starts with an amplitude of 16.0 cm, and 60.0 s later the amplitude has fallen to 8.0 cm. The decay is such that equal time intervals produce equal fractional loss. After a further 60.0 s, the amplitude and the energy expressed as a fraction of the starting energy are:
Show answer and why every option is right or wrong
Answer: B. B is correct: equal fractional loss in equal intervals means the amplitude halves again, from 8.0 cm to 4.0 cm, and since energy goes as amplitude squared, (4.0/16.0)² = 1/16 of the starting energy remains (NCERT Physics Lab Manual Class 11, Part 9, page 148).
Why A is wrong: A is wrong on the energy: the amplitude ratio is 1/4, and squaring it gives 1/16, not 1/8.
Why C is wrong: C is wrong on the amplitude: 2.0 cm would need a third 60.0 s interval, not a second.
Why D is wrong: D is wrong: it repeats the amplitude already reached at 60.0 s and reports the energy fraction belonging to that earlier instant.
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How do you solve a Experiment 03 Simple Pendulum Damping question? A worked example
- 1
Given
A simple pendulum is set swinging with a small initial displacement. Its initial amplitude is A₀ = 10.0 cm. After a time t₁ = 1.20 × 10² s the amplitude is measured as A₁ = 5.0 cm. The time period throughout is T = 2.0 s, constant to the precision used, and the oscillation count is the clock.
- 2
Required
(i) the fraction of the original energy remaining at t₁; (ii) the number of complete oscillations elapsed by t₁.
- 3
Concept
For small-angle oscillation the total mechanical energy is proportional to the square of the amplitude, so an energy ratio comes from an amplitude ratio by squaring it. The time coordinate of any reading is the number of counted oscillations multiplied by the time period, because damping leaves the period effectively unchanged while the amplitude decays (NCERT Physics Lab Manual Class 11, Part 9, page 149).
4. Relation used: E ∝ A², therefore E₁/E₀ = (A₁/A₀)². And t = n × T, where n is the counted number of complete oscillations. - 5
Substitution
E₁/E₀ = (5.0 cm / 10.0 cm)². n = t₁ / T = (1.20 × 10² s) / (2.0 s).
- 6
Calculation
(5.0/10.0)² = (0.50)² = 0.25. n = 1.20 × 10² / 2.0 = 60 oscillations. The exponent 2 in E ∝ A² is a counting number and n is an exact integer count; neither contributes to the significant-figure count. The reported precision follows the measured amplitudes and time, each given to two significant figures.
- 7
Final answer
One quarter of the original energy remains, E₁/E₀ = 0.25, and 60 complete oscillations (exact count) have elapsed.
- 8
Common trap
Reading "the amplitude has halved" as "the energy has halved". The amplitude ratio must be squared before it becomes an energy ratio — precisely the step the A²-versus-time plot exists to make visible.
- 9
Similar NEET-style question
A damped pendulum's amplitude falls from 9.0 cm to 3.0 cm over some interval. What fraction of its energy has been dissipated in that interval? (Answer: (3.0/9.0)² = 1/9 remains, so 8/9 has been dissipated.)
What to remember before solving Experiment 03 Simple Pendulum Damping questions
More in Experimental Skills: 6 exam traps and mistakes · 3 formulas · 1 question pattern from its other lessons.
Experiment 03 Simple Pendulum Damping questions from past NEET papers
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Sources
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