NEET · Physics
Own the oscillation/SHM portion of official Unit 10: periodic motion, period/frequency/phase, ideal SHM equation, spring oscillator, SHM energy and simple pendulum with small-angle conditions.
In short
Oscillations covers periodic motion and the ideal simple-harmonic model. SHM requires acceleration proportional to displacement and directed toward equilibrium, a=-ω^2x. The simple-pendulum period formula requires the small-angle approximation and an ideal pendulum model; it is not valid unchanged for large amplitudes.
Subject faculty
Also in Physics: Kumar Gandharva Saxena
Periodic motion repeats after a time interval. SHM is a special oscillatory motion in which the restoring acceleration is proportional to displacement and opposite in direction. The page must prevent students from labeling every periodic motion as SHM.
If displacement is sinusoidal, velocity is shifted in phase relative to displacement and acceleration is exactly opposite in phase to displacement. At equilibrium, speed is maximum in ideal SHM; at extreme displacement, speed is zero and restoring acceleration magnitude is maximum.
For an ideal mass-spring oscillator with a light spring obeying Hooke's law, ω=sqrt(k/m) and the period follows. Real damping and nonlinear spring behavior are outside the ideal formula.
For a point mass suspended by a light inextensible string of length L in uniform gravity, the exact restoring term involves sinθ. The standard period formula uses sinθ≈θ with angle in radians, requiring small oscillations.
SHM displacement: x = A cos(ωt+φ). m. Ideal SHM; A amplitude, ω rad s^-1, φ phase constant.
SHM displacement
Use when — m. Ideal SHM; A amplitude, ω rad s^-1, φ phase constant.
SHM acceleration: a = -ω^2 x. m s^-2. Defining dynamical signature of ideal SHM.
SHM acceleration
Use when — m s^-2. Defining dynamical signature of ideal SHM.
SHM speed relation: v^2 = ω^2(A^2-x^2). m^2 s^-2. Ideal SHM.
SHM speed relation
Use when — m^2 s^-2. Ideal SHM.
Period/frequency: T=2π/ω, f=1/T. s and Hz. ω=2πf.
Period/frequency
Use when — s and Hz. ω=2πf.
Mass-spring period: T = 2π sqrt(m/k). Ideal light spring, Hooke-law linearity, effective mass assumptions as stated; k N m^-1.
Mass-spring period
Use when — Ideal light spring, Hooke-law linearity, effective mass assumptions as stated; k N m^-1.
SHM total energy spring: E=(1/2)kA^2. J. Ideal undamped Hooke-law oscillator.
SHM total energy spring
Use when — J. Ideal undamped Hooke-law oscillator.
Simple pendulum period: T = 2π sqrt(L/g). Small-angle oscillations, point bob, light inextensible string, uniform g, negligible damping.
Simple pendulum period
Use when — Small-angle oscillations, point bob, light inextensible string, uniform g, negligible damping.
Concept being tested: Mass-spring period
Prompt: An ideal mass 0.25 kg is attached to a spring of constant 100 N m^-1. Find the SHM period.
Decisive condition: The spring is ideal and Hooke-law conditions are implied, so use T=2πsqrt(m/k).
Method choice: Substitute m/k=0.25/100=0.0025 s^2.
Reasoning/calculation: T=2π×0.05=0.1π≈0.314 s.
Unit/sign/condition check: Seconds are correct because m/k has dimension s^2.
PI if answered incorrectly: Execution Error if the square root is missed; Decision / Selection Error if non-Hookean behavior is ignored.
Calling every periodic motion SHM
Knowledge gapWhy it happens
Preparation Intelligence classification: Knowledge Gap.
How it is corrected
Check whether a is proportional to -x.
Using pendulum period at large amplitude without caveat
Decision / selection errorWhy it happens
Preparation Intelligence classification: Decision / Selection Error.
How it is corrected
Require the small-angle approximation.
Saying acceleration is zero at extreme displacement
Recall gapWhy it happens
Preparation Intelligence classification: Recall Gap.
How it is corrected
Speed is zero there; acceleration magnitude is maximum.
Using spring formula beyond the Hooke-law region
Decision / selection errorWhy it happens
Preparation Intelligence classification: Decision / Selection Error.
How it is corrected
Check linear restoring-force condition.
FAQ
Straight answers about how Rank Sarthi fits into serious exam preparation.
Acceleration is proportional to displacement and directed toward equilibrium: a=-ω^2x.
For small-angle oscillations of the ideal simple pendulum.
At equilibrium.
Official scope is taken from the NEET (UG) 2026 syllabus and official NTA documents; concept structure follows current NCERT contents. No performance, weightage or question-frequency data is asserted.
