NEET Physics · Chapter 16
Displacement in S.H.M. – Complete Notes, Revision, Important Questions & Downloads
This topic is built around one TOC subtopic, Displacement Equations, and NEET tests whether you can choose the correct sinusoidal form from the starting condition. From the projection picture of uniform circular motion, displacement is tracked from the mean position or the extreme position, so phase choice is the whole game. NEET tests this topic through condition-to-equation selection, phase-offset interpretation, and quick displacement evaluation at standard time fractions. Questions usually ask which equation matches an initial state, or ask displacement at a given time using y = a sin(omega t), y = a cos(omega t), or y = a sin(omega t +/- phi).
Condition-Based Equation ChoicePhase LogicNCERT-Linked
Expected QuestionsQ
1
Usually one direct question or one embedded step in an SHM multi-part problem where initial condition decides the equation form.
Time Required⏱
1.5 h
45 min concept build from projection model + 45 min condition-to-equation drills.
Difficulty⚡
Easy-Medium
Formulas are short, but sign and phase interpretation errors are frequent under timed solving.
NRI USA Curriculum GapUS
Bridge Needed
US high-school treatment often stops at graph intuition; NEET expects fast algebraic switching between sine, cosine, and phase-shifted forms.
9Subtopics
24Practice Questions
4Free Downloads
1.5 hPrep Time
Displacement in S.H.M. Weightage and Question Trend
Simple Harmonic Motion · Topic 2| NEET Year | Questions from this Topic | Bar | Marks |
|---|---|---|---|
| 2020 | 1 | 4 | |
| 2021 | 1 | 4 | |
| 2022 | 1 | 4 | |
| 2023 | 1 | 4 | |
| 2024 | 1 | 4 | |
| 2025 | 1 | 4 | |
| Topic-linked asks in the last 6 NEET sets | 6 | 24 |
The most common ask is initial-condition decoding: mean position start maps naturally to sine form, while extreme-position start maps to cosine form.
Phase-offset form y = a sin(omega t +/- phi) appears when the particle is already leading or lagging at t = 0.
Students lose marks by using the right amplitude but wrong reference instant, producing the wrong trigonometric function.
Phase-offset form y = a sin(omega t +/- phi) appears when the particle is already leading or lagging at t = 0.
Students lose marks by using the right amplitude but wrong reference instant, producing the wrong trigonometric function.
1.0
Avg Questions / Year
24
Total Marks (6 yrs)
Direct
Pattern
Medium
Difficulty
5-Step Displacement Equation Selection Routine
1
Fix the Reference Instant Before touching options, write whether t = 0 is at mean position, extreme position, or some phase-shifted state. Equation choice depends on this line alone.
2
Lock the Base Form Use y = a sin(omega t) for mean-position start and y = a cos(omega t) for extreme-position start, then add phase only if the prompt says leading or lagging.
3
Check Amplitude and Sign Together Ensure |y| never exceeds a and the sign at the stated instant matches physical location relative to mean position.
4
Translate Projection Language If the stem mentions projection of uniform circular motion on a diameter, map angular position to phase angle directly instead of guessing from memory.
5
Run a Quick Boundary Test Substitute t = 0 and t = T/4 mentally to see whether displacement sequence matches the described motion direction and starting point.
Displacement in S.H.M. Download Kit
PDF · Cheat Sheet · MCQ Set · PYQFull Notes
Complete topic notes on displacement equations with condition mapping, phase interpretation, and worked examples from SHM projection setups.
Download PDFFormula Sheet
One-page displacement equation map covering y = a sin(omega t), y = a cos(omega t), and phase-shift forms with start-condition triggers.
Download PDFMCQ Practice
Condition-based MCQ set focused on selecting the correct displacement equation from initial position and phase information.
Download PDFPYQ Workbook
Year-tagged SHM displacement and phase questions with concise solution logic and trap analysis for wrong equation selection.
Download PDFSubtopics in Displacement in S.H.M.
2-Column TableRapid Revision Cards
Concept → Trap → Example1) Displacement Equations
Core SHM formDisplacement in SHM is measured from mean position and can be written as y = a sin(omega t), y = a cos(omega t), or y = a sin(omega t +/- phi) depending on starting condition.
- Use sine form when time counting starts at mean position with displacement initially zero.
- Use cosine form when time counting starts at extreme position where displacement magnitude is maximum.
- Trap: selecting formula only from memory without matching it to the stated initial phase or reference instant.
Example (NEET-style)If amplitude a = 5 cm and the particle starts from mean position at t = 0, displacement after T/4 is y = 5 sin(pi/2) = 5 cm. If the same particle starts from extreme position, the matching form is y = 5 cos(omega t), not sine.
US Curriculum Gaps - Displacement in S.H.M.
Students need to bridge from graphical intuition to condition-based equation selection under timed MCQ constraints.AP Physics 1 to NEET Initial-Condition Translation Gap
AP Physics 1 often develops SHM with qualitative graph discussion, but NEET expects immediate conversion of initial position and direction into the correct displacement equation.
- Practice 25 stems where only the initial state changes and equation form must be chosen in under 20 seconds.
- Train phase-language parsing: leading, lagging, and reference instant wording.
- Check answer by substituting t = 0 to verify physical start point before final marking.
Algebra-Based Physics to NEET Phase-Sign Discipline Gap
Typical Algebra-Based Physics courses cover SHM equations, but NEET one-correct MCQs penalize small sign and phase mistakes more aggressively.
- Maintain a fixed sign convention for displacement from equilibrium across all practice sets.
- Use short boundary checks at t = 0 and t = T/4 to reject inconsistent options quickly.
- Build a phase notebook of recurring trap patterns from mixed SHM questions.
Concept IQ Check
4 NEET-style MCQs with Answers1A particle executes SHM of amplitude 4 cm. Time is measured from the instant when the particle is at mean position and moving toward positive displacement. Which displacement equation is correct?Condition mapping
y = 4 cos(omega t)
y = 4 sin(omega t)
y = 4 sin(omega t + pi/2)
y = -4 sin(omega t)
At t = 0, the particle is at mean position, so displacement must be zero. The option must also represent motion initially toward positive y, which requires positive slope at t = 0. For y = 4 sin(omega t), y(0)=0 and dy/dt at t=0 is +4omega, so both conditions are satisfied. y = 4 cos(omega t) gives y(0)=4 cm, which is extreme position, not mean. y = 4 sin(omega t + pi/2) is equal to 4 cos(omega t), again wrong start. y = -4 sin(omega t) gives negative initial velocity, opposite to the stated direction.
2An SHM particle starts from extreme positive position at t = 0 with amplitude a. Which equation correctly represents displacement?Extreme start
y = a cos(omega t)
y = a sin(omega t)
y = -a cos(omega t)
y = a sin(omega t - pi/2)
For an extreme positive start, the displacement at t = 0 must be +a and instantaneous velocity must be zero. y = a cos(omega t) directly gives y(0)=a and dy/dt = -a omega sin(omega t), which is zero at t=0. y = a sin(omega t) gives y(0)=0, so it corresponds to mean-position start. y = -a cos(omega t) gives y(0)=-a, the opposite extreme. y = a sin(omega t - pi/2) equals -a cos(omega t), so it again starts at negative extreme. This is a standard NEET trigger where start condition immediately fixes cosine form and sign.
3A particle executes SHM with y = 6 sin(omega t + pi/6) cm. The phase constant indicates that at t = 0 the particle is:Phase shift
at mean position
at extreme positive position
at displacement 3 cm on positive side
at displacement -3 cm on negative side
Substitute t = 0 into y = 6 sin(omega t + pi/6): y(0)=6 sin(pi/6)=3 cm, positive. Therefore the particle is neither at mean position (which would require y=0) nor at extreme positive (which requires y=+6 cm). The negative-displacement option is sign-inconsistent. This style checks whether students can read phase as initial angular location rather than treating phi as a decorative constant. In many one-correct questions, the full solution is a one-line substitution at t=0, but only if sign and trig value are handled correctly.
4A particle has displacement y = a sin(omega t). What is its displacement after time T/2 from t = 0?Time substitution
+a
0
-a
a/2
Use omega = 2pi/T, so at t = T/2, argument is omega t = pi. Then y = a sin(pi) = 0. This shows that in sine-start SHM, the particle returns to mean position after half a period, though velocity direction reverses. +a and -a correspond to quarter-cycle extremes depending on phase. a/2 has no basis at this time instant. Such MCQs reward clean mapping between time fractions and trigonometric arguments, and they also expose students who memorize displacement values without connecting them to omega t.
Practice Questions - Displacement in S.H.M.
Click "Reveal Answer" after attempting1A particle executes SHM with amplitude 8 cm and starts from mean position moving in positive direction. Find displacement at t = T/6.
4 cm
4sqrt(3) cm
8 cm
-4 cm
👁 Reveal Answer
Correct option: 1. For mean-position start, y = a sin(omega t). At t = T/6, omega t = 2pi/6 = pi/3. Therefore y = 8 sin(pi/3) = 8 x (sqrt(3)/2) = 4sqrt(3) cm. Wait, this matches option 2; hence option 2 is correct. This is why trig substitution must be done before marking quickly.
2A particle starts from extreme position with amplitude 10 cm. Using the correct equation, find displacement at t = T/3.
5 cm
-5 cm
0 cm
10 cm
👁 Reveal Answer
Correct option: 2. Extreme-position start uses y = a cos(omega t). At t = T/3, omega t = 2pi/3. So y = 10 cos(2pi/3) = 10 x (-1/2) = -5 cm. Option 1 has wrong sign, option 3 corresponds to mean position, and option 4 is only at t = 0. The negative value indicates particle is on the opposite side of equilibrium at that instant.
3For y = 5 sin(omega t + pi/6) cm, what is displacement at t = 0?
0 cm
2.5 cm
5 cm
-2.5 cm
👁 Reveal Answer
Correct option: 2. Substituting t = 0 gives y(0) = 5 sin(pi/6) = 5 x 1/2 = 2.5 cm. This direct substitution is a standard way to decode initial position from phase constant. Option 1 is only for zero phase sine start, option 3 is for positive extreme, and option 4 has incorrect sign.
4A particle is described by y = a sin(omega t). Which statement is true at t = T/4?
y = 0
y = +a
y = -a
y = a/2
👁 Reveal Answer
Correct option: 2. At t = T/4, omega t = 2pi/T x T/4 = pi/2. Therefore y = a sin(pi/2) = a. So the particle is at positive extreme displacement. Option 1 belongs to t = 0 or T/2; option 3 belongs to 3T/4; option 4 does not correspond to this phase angle.
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FAQ - Displacement in S.H.M.
Notes · Downloads · Revision · Important QuestionsWhy does mean-position start usually give y = a sin(omega t) and not cosine?
Because at mean position displacement must be zero at t = 0. Sine naturally gives y(0) = 0, while cosine gives y(0) = a. If the question also says motion initially toward positive side, dy/dt at t = 0 must be positive, which y = a sin(omega t) satisfies. Always test both displacement and initial direction before finalizing the form.
When should I use y = a cos(omega t) in NEET problems?
Use cosine when time is measured from an extreme position. Then y(0) must be +a or -a depending on side, and velocity is zero at start. A common trap is selecting sine from habit even when the stem explicitly says 'starts from extreme position'. First line in rough work should be the starting position at t = 0.
What does the phase constant phi physically represent in displacement equations?
It fixes where the particle is in its cycle at t = 0, i.e., the initial angular location in the reference circle picture. In y = a sin(omega t + phi), setting t = 0 gives initial displacement a sin(phi). So phi is not an optional constant; it encodes initial condition and decides sign and magnitude at the start.
How do I quickly detect a wrong option among displacement equations?
Substitute t = 0 first. If the resulting displacement contradicts the stated initial position, reject immediately. Next check one more instant, usually T/4, to test trend direction. This two-point filter is faster and safer than memorizing many formula variants, especially in one-correct MCQs with close-looking options.
Does displacement in SHM mean distance travelled from start point?
No. In this context, displacement is measured from mean (equilibrium) position at that instant. Distance travelled is path length and is always non-negative; SHM displacement can be positive or negative depending on side. NEET often designs distractors by mixing these two ideas, so keep the reference point explicit in your rough work.
Why is the projection of uniform circular motion useful for displacement in SHM?
It gives a geometric way to read phase and write the displacement equation. The projection on a diameter directly produces sinusoidal variation, and the angular position of the rotating radius gives phase. This model helps interpret phase-leading and phase-lagging statements without confusion and reduces sign errors in equation selection.
Can one SHM motion be written by both sine and cosine forms?
Yes, because sine and cosine differ by a phase shift. For example, a cos(omega t) = a sin(omega t + pi/2). The physical motion is the same if phase is adjusted correctly. In exams, wrong options usually keep amplitude correct but use an inconsistent phase that fails the given initial condition when t = 0 is substituted.
What is the most common error in displacement-based SHM numericals?
Students often ignore the phrase that defines the time origin, such as 'time measured from mean position' or 'from extreme position'. That single phrase decides the base equation. A close second error is incorrect trig value at standard angles. To avoid both, write omega t value explicitly and evaluate with known angle values before choosing the option.
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