Class 11 — Oscillations

Chapter Overview & Weightage

Oscillations sits squarely in the middle of the Class 11 mechanics block and is one of the most predictable scoring chapters in the CBSE physics paper. The chapter is short, the formulas are limited, and the questions follow a tight pattern year after year. If you have done Newton’s laws and energy conservation, you already have $80\%$ of what you need.

Typical CBSE weightage: $5-7$ marks per year, usually one $3$ -mark numerical (period of pendulum/spring) and one $2$ -mark conceptual or graph question. Occasionally a $5$ -mark derivation appears in years when the paper is heavy on mechanics.

Year	Marks	Question type
2019	5	Derive expression for time period of simple pendulum
2020	3	Numerical: spring-mass system
2021	5	SHM equation + graph
2022	3	Numerical: simple pendulum length
2023	5	Energy in SHM derivation
2024	3	Numerical: damped vs undamped oscillator

Key Concepts You Must Know

Definition of SHM as motion under restoring force proportional to displacement
Equation $x(t) = A\sin(\omega t + \phi)$ and its derivatives for $v(t)$ and $a(t)$
Time period of spring-mass system: $T = 2\pi\sqrt{m/k}$
Time period of simple pendulum: $T = 2\pi\sqrt{L/g}$
Energy in SHM: total = kinetic + potential = $\tfrac{1}{2}m\omega^2 A^2$
Phase, phase difference, and how to read SHM graphs
Forced oscillations and resonance (qualitative for boards)
Damped oscillations: amplitude decays exponentially

Important Formulas

$x(t) = A\sin(\omega t + \phi), \quad v = A\omega\cos(\omega t + \phi), \quad a = -\omega^2 x$

Use these to relate position, velocity, and acceleration at any time.

$T_{\text{spring}} = 2\pi\sqrt{m/k}, \quad T_{\text{pendulum}} = 2\pi\sqrt{L/g}$

Apply to find period from given mass/length, or to find unknown $g$ in physics-lab questions.

$E = \tfrac{1}{2}m\omega^2 A^2 = \tfrac{1}{2}kA^2$

Total energy is constant. KE max at $x=0$ , PE max at $x=\pm A$ .

$v = \omega\sqrt{A^2 - x^2}$

Use this to find speed without needing to know time. Derived from energy conservation.

Solved Previous Year Questions

PYQ 1 (CBSE 2022, 3 marks)

A simple pendulum has time period $2$ s on Earth where $g = 9.8\,\text{m/s}^2$ . Find its time period on the Moon where $g_m = 1.6\,\text{m/s}^2$ .

Since $T \propto 1/\sqrt{g}$ , the ratio $T_m/T_e = \sqrt{g_e/g_m} = \sqrt{9.8/1.6} = \sqrt{6.125} \approx 2.475$ .

$T_m = 2 \times 2.475 = 4.95$ s $\approx 4.95$ s.

PYQ 2 (CBSE 2023, 5 marks)

Show that for SHM, total mechanical energy is conserved. Prove it for a spring-mass system.

KE = $\tfrac{1}{2}mv^2 = \tfrac{1}{2}m\omega^2(A^2 - x^2)$ (using $v = \omega\sqrt{A^2 - x^2}$ ).

PE = $\tfrac{1}{2}kx^2 = \tfrac{1}{2}m\omega^2 x^2$ (using $\omega^2 = k/m$ ).

Sum = $\tfrac{1}{2}m\omega^2 A^2$ — independent of $x$ . Hence conserved.

PYQ 3 (CBSE 2020, 3 marks)

A spring of force constant $200$ N/m carries a $0.5$ kg mass. Find the time period and frequency.

$T = 2\pi\sqrt{m/k} = 2\pi\sqrt{0.5/200} = 2\pi \times 0.05 = 0.314$ s.

$f = 1/T = 3.18$ Hz.

Difficulty Distribution

Difficulty	% of CBSE Qs	Typical type
Easy	$40\%$	Direct formula plug-in (period, frequency)
Medium	$45\%$	Energy split, graph reading, derivations
Hard	$15\%$	Combined SHM + Newton’s law, physical pendulum

Expert Strategy

For this chapter, derive all formulas at least once on paper. CBSE often asks “Derive expression for time period of…” — having done it twice from scratch makes the 5-mark question a freebie.

Memorise the energy formula $E = \tfrac{1}{2}m\omega^2 A^2$ . Most “energy at this displacement” questions are one-line plug-ins from this.

For graph-based questions, remember: $v(t)$ leads $x(t)$ by $\pi/2$ , $a(t)$ leads $v(t)$ by $\pi/2$ . Cosine graphs come from $a$ , sine graphs come from $x$ (with $\phi = 0$ ).

Common Traps

Confusing angular frequency $\omega$ with frequency $f$ . Always: $\omega = 2\pi f$ . Forgetting the $2\pi$ is the most common error in spring-mass problems.

Treating the pendulum period formula as valid for any angle. $T = 2\pi\sqrt{L/g}$ is for small oscillations only ( $\theta < 10^\circ$ ). For larger angles, the period increases — but this is beyond CBSE 11 scope, so don’t volunteer it on board exams.

Saying “at extreme position, both KE and PE are maximum”. KE is zero at extremes (velocity is zero). PE is maximum. Energy is fully potential at the turning points.

For the full conceptual treatment with practice questions, our oscillations hub covers SHM in depth with worked examples.