Complete formula sheet, NCERT-style examples, CBSE, NEET, JEE Main, JEE Advanced, IB, IGCSE, A-Level questions, assertion-reason, case studies and quick revision notes.
Use this page as a final revision sheet. Each formula is written in PHYSICS form with symbol meaning, unit sense and exam use. The most common mistake in Oscillations is using the correct-looking formula in the wrong situation, so read the exam-use line carefully.
Symbols and units: a is acceleration, ω is angular frequency, x is displacement from mean. Unit of a is m s−2.
Exam use: Use this to identify SHM. If acceleration is proportional to displacement and opposite in direction, motion is SHM.
Symbols and units: T is time period in seconds and f is frequency in Hz. Unit of ω is rad s−1.
Exam use: Use to convert between time period, frequency and angular frequency.
Symbols and units: f is number of oscillations per second. Unit is Hz.
Exam use: Use in direct MCQs and graph-based questions.
Symbols and units: A is amplitude. Unit is m s−1.
Exam use: Use at mean position where x = 0.
Symbols and units: A is amplitude. Unit is m s−2.
Exam use: Use at extreme positions where x = ±A.
Symbols and units: φ is initial phase. x is displacement.
Exam use: Use when initial position and direction are given.
Symbols and units: Starts from mean position and initially moves in positive direction.
Exam use: Use for standard graph questions.
Symbols and units: Velocity leads displacement by π/2 for x = A sin(ωt).
Exam use: Use to draw v-t graph correctly.
Symbols and units: Acceleration is opposite in phase to displacement.
Exam use: Use to draw a-t graph and compare phases.
Symbols and units: Speed depends on position, maximum at mean and zero at extremes.
Exam use: Very important for NEET and JEE numericals.
Symbols and units: Phase tells the state of oscillation at an instant. Unit is radian.
Exam use: Use to compare two oscillations.
Symbols and units: Positive or negative sign indicates lead or lag.
Exam use: Use in graph comparison and wave-SHM analogy.
Symbols and units: Velocity leads displacement by π/2.
Exam use: Use in phase relation MCQs.
Symbols and units: Acceleration differs from displacement by π.
Exam use: Use to remember a is opposite in phase with x.
Symbols and units: Convert phase difference to time difference.
Exam use: Useful in JEE Main conceptual numericals.
Symbols and units: k is spring constant in N m−1.
Exam use: Use Hooke law and identify restoring force.
Symbols and units: m is attached mass in kg.
Exam use: Use for horizontal or vertical spring about equilibrium.
Symbols and units: Time period increases with mass and decreases with stiffness.
Exam use: Most common spring formula.
Symbols and units: Frequency of spring block.
Exam use: Use when asked oscillations per second.
Symbols and units: y is static extension with mg = ky.
Exam use: Useful shortcut for vertical spring problems.
Symbols and units: If spring of constant k is cut into n equal parts, each part has constant nk.
Exam use: Do not write k/n. Shorter spring is stiffer.
Symbols and units: Using one cut part with same mass.
Exam use: Important JEE trap.
Symbols and units: Series combination is softer.
Exam use: Use when same force passes through springs.
Symbols and units: Parallel combination is stiffer.
Exam use: Use when extensions are same.
Symbols and units: Both springs give restoring force toward mean.
Exam use: Use T = 2π√(m/(k1 + k2)).
Symbols and units: L is effective length in m, g in m s−2.
Exam use: Valid for small angular displacement.
Symbols and units: Frequency increases when g increases and decreases when length increases.
Exam use: Use in clock questions.
Symbols and units: For spherical bob, include radius if string length is to top of bob.
Exam use: Common practical exam trap.
Symbols and units: Time from one extreme to the other is 1 s.
Exam use: Approximate length near Earth is about 1 m.
Symbols and units: Needed for pendulum SHM.
Exam use: Large-angle pendulum is not exactly SHM.
Symbols and units: K is maximum at mean and zero at extremes.
Exam use: Use for energy-position questions.
Symbols and units: U is zero at mean and maximum at extremes.
Exam use: Do not make U negative in basic SHM energy graphs.
Symbols and units: Total energy remains constant in ideal SHM.
Exam use: Use conservation of energy.
Symbols and units: At this displacement, each energy is E/2.
Exam use: Very common MCQ.
Symbols and units: K and U repeat twice in one oscillation, total energy does not oscillate.
Exam use: High-yield graph concept.
Symbols and units: Damping force is opposite to velocity.
Exam use: Use in damped oscillation basics.
Symbols and units: External periodic driving force.
Exam use: Use to distinguish driving frequency from natural frequency.
Symbols and units: Driving frequency nearly equals natural frequency for light damping.
Exam use: Use in resonance applications.
Symbols and units: Q is dimensionless.
Exam use: High Q means sharp resonance and low damping.
Symbols and units: f1 and f2 are half-power frequencies.
Exam use: Use in JEE graph/numerical questions.
SHM x-t, v-t, a-t Graphs
Spring Block System
Cut Spring: k' = nk
Springs in Series and Parallel
Simple Pendulum
Energy in SHM
Resonance Curve
Block Between Two Springs
These questions follow the NCERT style: direct formulas, unit sense, simple substitutions and conceptual checks.
vmax = Aω = 0.05 × 4 = 0.20 m/s.
v2 = ω2(A2 − x2) = 100(0.0025 − 0.0009) = 0.16, so v = 0.4 m/s.
T = 2π√(m/k) = 2π√(1/100) = π/5 s.
T = 2π√(L/g) = 2 s.
T ∝ √L, so time period becomes 2 times.
E ∝ A2, so energy becomes 4 times.
K = U gives A2 − x2 = x2, so x = ±A/√2.
Each part has k' = nk = 4k.
T' = T/√n = 6/3 = 2 s.
keff = k1 + k2 = 200 N/m.
At extreme x = ±A, U = E and K = 0.
Kinetic energy repeats after T/2 because it depends on speed squared.
If Oscillations formulas or PYQs are not clear and you are looking for a Physics Tutor, contact Kumar Sir.
Includes CBSE, NEET, JEE Main, JEE Advanced, IB, IGCSE, A-Level, assertion-reason, true/false, case study, conceptual and difficult numerical questions.
Acceleration must be directly proportional to displacement and opposite in direction: a = −ω2x.
x = A sin(ωt + φ).
π radian. They are opposite in phase.
Time period is time for one complete oscillation. Frequency is number of oscillations per second.
E = ½mω2A2.
Kinetic energy is maximum and potential energy is minimum.
Zero.
Four times.
Mass m and spring constant k.
Mass of bob and small amplitude.
3 times.
4k.
T' = T/√n.
x = ±A/√2.
T/2.
v = Aω cos(ωt).
a = −Aω2 sin(ωt).
v2 = ω2(A2 − x2).
k/2.
2k.
k1 + k2.
T = 2π√(m/(k1 + k2)).
T = 2π√(y/g).
2 s.
1 s.
keq = k/3, so T' = √3 T.
keq = 3k, so T' = T/√3.
k' = 4k and m' = 4m, so T remains same.
Acceleration leads velocity by π/2 and differs from displacement by π.
x2/A2 + v2/(A2ω2) = 1.
a = −ω2x.
Energy changes form between kinetic and potential, but their sum stays constant without damping.
Difference between phases of two oscillations or two quantities in the same oscillation.
Measure time for many oscillations and divide by number of oscillations.
No change for small oscillations.
Because sin θ ≈ θ only for small angles.
Sharp resonance, low damping and narrow bandwidth.
Both are true and reason explains assertion.
Both are true and reason explains assertion.
Assertion is false; reason is true but mass cancels.
False. Total energy is constant; no oscillation.
False. It is minimum at mean position.
True.
True.
False. Damping limits amplitude.
Length increases due to thermal expansion, so period increases and clock runs slow.
To remove energy and reduce repeated oscillations after bumps.
Electrical resonance and frequency selectivity.
K = ½mv2, and square of velocity is non-negative.
U = ½kx2, and square of displacement is non-negative.
K/E = (A2 − x2)/A2 = (100 − 36)/100 = 0.64.
Q = 500/20 = 25.
T' = T/√16 = T/4.
keq = 4k, so T' = T/2.
keq = k/4, so T' = 2T.
T ∝ 1/√g, so T becomes 2T.
T ∝ √m, so T becomes 3T.
T ∝ 1/√k, so period becomes T/3.
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