# Oscillations > Oscillations for NEET-UG Physics — simple harmonic motion formulae, spring and pendulum periods, energy exchange, damping and resonance. - Canonical URL: https://prepelephant.com/topics/neet-ug/physics/oscillations-ncert - Exam / course: NEET-UG · Subject: Physics - Publisher: PrepElephant (https://prepelephant.com) — Prepared and reviewed by the PrepElephant Academic Review Team - First published: 2026-10-02 - Last updated: 2026-10-02 - How to cite: "Oscillations", PrepElephant, https://prepelephant.com/topics/neet-ug/physics/oscillations-ncert ## Direct answer Pull a mass on a spring to one side and release it: the acceleration always points back toward the mean position with a = -ω^2x, and that is simple harmonic motion — sinusoidal, isochronous (period independent of amplitude), and the model behind pendulums, vibrating strings and half of acoustics. The two systems NEET-UG actually examines are the spring-mass oscillator, T = 2π sqrt(m/k), and the small-angle pendulum, T = 2π sqrt(l/g), followed by damped motion and resonance. ## What you must remember - x(t) = A sin(ωt + φ): speed is maximum (Aω) at the mean position where displacement and acceleration are zero; acceleration is maximum (Aω^2) at the extremes where speed is zero. - Spring-mass period T = 2π sqrt(m/k): heavier oscillates slower, stiffer springs faster; amplitude has no say (for ideal SHM). - Simple pendulum T = 2π sqrt(l/g): independent of the bob's mass; the seconds pendulum (T = 2 s) needs a length of about one metre. - Total energy E = (1/2)kA^2 = (1/2)mω^2A^2, sloshing between kinetic (max at the centre) and potential (max at the extremes); the two are equal at x = ±A/sqrt(2). - Timing facts: mean position to an extreme takes T/4; extreme to extreme T/2; a full out-and-back T. - Damped oscillations decay in amplitude (energy leaks to friction); critical damping returns the system to rest fastest without oscillating — the dead-beat galvanometer design. - Forced oscillations respond to a driving frequency; resonance — driving frequency equal to natural frequency — makes the amplitude peak sharply when damping is small, which is why troops break step over bridges. - SHM is the projection of uniform circular motion, so ω in SHM carries the same meaning as angular speed in that circle. ## Worked example: energy audit of an oscillator A 2 kg block on a spring of stiffness 200 N/m is pulled 10 cm from equilibrium and released. The angular frequency is ω = sqrt(k/m) = sqrt(200/2) = 10 rad/s, so the period is T = 2π/10 ≈ 0.63 s — note how neither the 10 cm nor any later amplitude appears in T. The total energy is E = (1/2)kA^2 = (1/2) × 200 × 0.01 = 1 J. At the halfway displacement x = 5 cm, the stored potential energy is (1/2) × 200 × (0.05)^2 = 0.25 J, so the kinetic energy there must be 0.75 J and the speed v = sqrt(2 × 0.75/2) ≈ 0.87 m/s. Cross-check with the kinematic formula v = ω sqrt(A^2 - x^2) = 10 × sqrt(0.01 - 0.0025) = 10 × 0.0866 = 0.87 m/s: the energy ledger and the motion formula agree exactly, and at the 0.707A displacement the split would be 50-50. Both routes to the same number is the habit that converts SHM questions into thirty-second answers. ## Where students slip "Heavier pendulum swings slower" — false; mass cancels in T = 2π sqrt(l/g), because the driving weight and the inertia it must move are the same m. The period-independence of amplitude holds only for small angles, where sin θ ≈ θ; swing the pendulum wide and the period lengthens, which is why the practical insists on amplitudes of a few degrees. In experiments, timing one oscillation multiplies reaction-time error by a factor of 20 relative to timing twenty and dividing — the exam states this as a percentage-error question. The damped case confuses students about period: weak damping barely shifts the frequency while the amplitude decays exponentially, so "damping changes the period noticeably" is false as stated. Finally, do not exchange ω and f: the mains of acoustics questions quote frequency in hertz, and ω = 2πf is the conversion SHM formulas silently assume. ## Frequently asked questions ### At what displacement are kinetic and potential energies equal in SHM? At x = A/sqrt(2) ≈ 0.707A, where each is half of the total (1/2)kA^2; at the centre all energy is kinetic, at the extremes all potential. ### Does a pendulum's period depend on the mass of the bob? No: T = 2π sqrt(l/g). Gravity pulls harder on a heavier bob, but the same extra mass resists acceleration, and the effects cancel. ### What is resonance? The driving frequency coincides with the system's natural frequency, so energy accumulates and the steady-state amplitude becomes very large when damping is small — sharpness of resonance falls as damping rises. ### Why does a pendulum clock taken from the hills to the equator run slow? g is smaller at the equator, so T = 2π sqrt(l/g) lengthens and each swing takes longer — the clock completes fewer swings per day and loses time. ### What is critical damping? The damping for which the system returns to equilibrium in the shortest time without oscillating — the design goal of vehicle shock absorbers and dead-beat galvanometers.