Oscillations

OscillationsNEET Physics · Class 11 · NCERT Chapter 13

Overview Notes NEET Questions Interactive Learning

7 interactive concept widgets for Oscillations. Drag any slider, change any number, and watch the formula and the answer update live. Built so you understand how each NEET problem actually works, not just the final number.

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SHM oscillator visualiser

SHM time period (spring and pendulum)

SHM as projection of circular motion

Energy in SHM (KE / PE bar)

Simple pendulum simulator

Series vs parallel springs

Damped oscillation curve

SHM core

A live SHM oscillator and the textbook time-period formula for spring-mass and simple pendulum.

SHM

SHM oscillator visualiser

A live particle in simple harmonic motion. Position, velocity and acceleration update in real time.

Watch a particle execute SHM. The position oscillates as x = A sin(omega t). The dashed lines mark x = +A and x = -A.

Amplitude A: 1.00 m

Time period T: 2.00 s

t = 0.00 s

0.000 m

3.142 m/s

0.000 m/s²

3.142 rad/s

x = A sin (ω t), v = A ω cos (ω t), a = - ω^{2} x

Try this

Pause and check: at x = 0 the particle moves fastest (v_max = A omega).
At x = ±A the particle is momentarily at rest, but acceleration is maximum (and points back to centre).
Halve the time period: omega doubles, v_max doubles, a_max quadruples.

Time period

SHM time period (spring and pendulum)

Two of the most-tested NEET formulas, side by side.

Two iconic SHM systems with the same kind of formula.

Mass m: 0.50 kg

Spring constant k: 50 N/m

Time period T

0.628 s

T = 2 π \frac{m}{k}

Angular freq ω

10.00 rad/s

Frequency f

1.592 Hz

Try this

Spring-mass: T does not depend on amplitude. Pendulum: only true for small angles.
On the moon (g ≈ 1.6 m/s²) a pendulum takes about 2.47x longer for the same length.
Stiffer springs (large k) shorten T; heavier mass (large m) lengthens T.
Doubling L on a pendulum increases T by sqrt(2) ≈ 1.41 times.

Phasor

SHM as projection of circular motion

The classic phasor picture: SHM is just the projection of uniform circular motion onto an axis.

SHM is the projection of uniform circular motion. The arrow rotates around the circle; its vertical projection traces a sine wave.

Time period T: 2.00 s

x (t) = A sin (ω t), ω = \frac{2 π}{T} ∣ angle = 0.00 rad, x = 0.000 A

Try this

The angular speed of the dot (omega) is the same as the angular frequency of the SHM.
Phase difference of pi/2 between two SHMs would show as the dot starting at the top vs starting on the right.
The radius of the circle equals the amplitude A.

Energy and pendulum

Energy split between KE and PE, plus a live simple pendulum.

Energy in SHM

Energy split between KE and PE

As the particle moves through SHM, kinetic and potential energy trade places. Their sum is the constant total energy.

Total energy is fixed at half k A squared. As the particle swings, energy moves between KE and PE; their sum always equals E.

Spring constant k: 100 N/m

Amplitude A: 0.100 m

Displacement x: 0.000 m

Energy split (total stays the same)

KE 100%

0.500 J

0.000 J

Total E

0.500 J

K E = \frac{1}{2} k (A^{2} - x^{2}), P E = \frac{1}{2} k x^{2}, E = \frac{1}{2} k A^{2}

Try this

At x = 0 (mean position): KE is maximum, PE is zero.
At x = ±A (extremes): KE is zero, PE is maximum (= E).
At x = A / sqrt(2): KE = PE = E / 2.

Pendulum

Simple pendulum simulator

A live pendulum with sliders for length, gravity and starting angle. Watch how T responds.

Watch a simple pendulum swing. For small angles, T is independent of mass and amplitude.

Length L: 1.00 m

g: 9.80 m/s² (Earth = 9.8, Moon = 1.6)

Initial angle θ₀: 15°

Time period

2.007 s

T = 2 π \frac{L}{g}

Try this

Quadruple L: T doubles. T scales as sqrt(L).
Switch g to 1.6 (moon): T grows by sqrt(9.8/1.6) ≈ 2.47 times.
Bob mass does NOT appear in the formula. A heavier bob keeps the same T.
Above about 15° the small angle approximation starts to break and T grows slightly.

Springs and damped oscillations

Series vs parallel springs, plus the exponentially decaying envelope of a damped oscillator.

Spring combinations

Series vs parallel springs

Two springs combine differently in series and in parallel. Compare the formulas and what they do to the time period.

Same two springs, two arrangements. The effective k changes, and so does the period.

k₁: 50 N/m

k₂: 100 N/m

Mass m: 0.50 kg

Effective spring constant

33.33 N/m

\frac{1}{k _{eff}} = \frac{1}{k _{1}} + \frac{1}{k _{2}}

Time period T

0.770 s

Try this

Series: effective k is SMALLER than the smaller of the two. The system is softer.
Parallel: effective k is LARGER than the larger of the two. The system is stiffer.
Two equal springs k in series: k_eff = k/2. In parallel: k_eff = 2k. Period changes by factor sqrt(2) or 1/sqrt(2).

Damped oscillation

Damped oscillation curve

The amplitude decays exponentially because of friction. Adjust the damping coefficient and watch the curve flatten.

Real oscillators slow down due to friction. Amplitude decays as e^(-b t), and the actual frequency is slightly less than omega_0 (the natural frequency).

Natural ω₀: 6.00 rad/s

Damping b: 0.40 1/s

Damped angular freq ω_d

5.99 rad/s

T_d = 1.05 s

ω_{d} = ω_{0}^{2} - b^{2}

Solid: x(t) = e^(-bt) cos(ω_d t). Dashed: amplitude envelope.

Try this

b = 0: pure SHM, amplitude does not decay.
Small b: oscillation persists but amplitude decays slowly.
b → ω₀: critical damping, no oscillation; the system returns to equilibrium fastest.
b > ω₀: overdamped; system creeps back without oscillating.

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