// PHYS//LAB Dashboard
Interactive Physics Simulation Laboratory
Classical Mechanics
Projectile motion, pendulums, springs, collisions, orbital mechanics with real-time free-body diagrams
5 SIMULATIONS
Electromagnetism
Electric field visualizer, Lorentz force trajectories, RLC circuit oscillation and resonance
3 SIMULATIONS
Waves & Optics
Wave superposition, double-slit interference, Fourier decomposition, ray optics with lenses
4 SIMULATIONS
Thermodynamics
Ideal gas law PV=nRT, Carnot heat engine cycles, statistical mechanics particle simulation
3 SIMULATIONS
// Projectile Motion
Classical Mechanics Β· Kinematics
PROJECTILE TRAJECTORY
M1
Parameters
40 m/s
45Β°
9.8 m/sΒ²
1.0 kg
Governing Equations
x(t) = vβΒ·cos(ΞΈ)Β·ty(t) = vβΒ·sin(ΞΈ)Β·t β Β½gtΒ²
Computed
Range: 0 mMax H: 0 m
T_flight: 0 s
// Pendulum
Classical Mechanics Β· Oscillations
SIMPLE & DOUBLE PENDULUM
M2
Mode
Parameters
140
100
90Β°
45Β°
0%
Simple Pendulum
ΞΈΜ = β(g/L)Β·sin(ΞΈ) β bΒ·ΞΈΜT β 2Οβ(L/g)
Energy
KE: 0 J PE: 0 J
// Spring-Mass System
Classical Mechanics Β· Hooke's Law
HARMONIC OSCILLATOR
M3
Parameters
20 N/m
2.0 kg
80 px
1.0
Equations of Motion
F = βkx β bαΊmαΊ + bαΊ + kx = 0
Οβ = β(k/m) = 3.16 rad/s
f = 0.50 Hz
ΞΆ = 0.16
// Collisions
Classical Mechanics Β· Momentum & Energy
1D ELASTIC & INELASTIC
M4
Type
Object A
5 kg
4 m/s
Object B
3 kg
-2 m/s
Conservation Laws
p = mβvβ + mβvβ = 26 kgΒ·m/sKE = 46 J
After Collision
vβ' = β m/svβ' = β m/s
// Orbital Mechanics
Classical Mechanics Β· Gravitation
KEPLER ORBITS & N-BODY
M5
Central Body
5000
Orbiter
150
3.5
Gravitational Force
F = GΒ·MΒ·m / rΒ²v_circ = β(GM/r)
Orbit Data
r = 150v = 3.5
E = β
// Electric Fields
Electromagnetism Β· Coulomb's Law
FIELD LINE VISUALIZER
E1
Add Charges (click canvas)
Display
16
4
Coulomb's Law
E = kQ/rΒ²k = 8.99Γ10βΉ NΒ·mΒ²/CΒ²
F = qE
Charges
Count: 0
// Lorentz Force
Electromagnetism Β· Charged Particle Motion
PARTICLE IN E + B FIELDS
E2
Fields
0
0
2.0
Particle
3.0
0
1.0
Lorentz Force
F = q(E + v Γ B)r_c = mv/(qB) = β
Ο_c = qB/m = β
// RLC Circuit
Electromagnetism Β· Oscillations & Resonance
DRIVEN RLC OSCILLATOR
E3
Components
50
100
10
Drive Signal
10 V
159
Resonance
fβ = 1/(2ΟβLC) = β HzQ = (1/R)β(L/C) = β
Z = β Ξ©
I = β A
// Wave Superposition
Waves & Optics Β· Interference
CONSTRUCTIVE & DESTRUCTIVE
W1
Wave 1
50
3.0
0Β°
Wave 2
50
3.0
0Β°
Superposition Principle
y = yβ + yβyβ = AβΒ·sin(kβx β Οβt + Οβ)
ΞΟ = 0Β°
// Double Slit Experiment
Waves & Optics Β· Interference Patterns
YOUNG'S DOUBLE SLIT
W2
Parameters
25
15
5
Interference Condition
dΒ·sinΞΈ = mΞ» (bright)dΒ·sinΞΈ = (m+Β½)Ξ» (dark)
Ξy = Ξ»L/d
// Fourier Decomposition
Waves & Optics Β· Signal Analysis
FOURIER SERIES BUILDER
W3
Target Waveform
Harmonics
5
Fourier Series
f(x) = aβ/2 + Ξ£[aβcos(nΟx) + bβsin(nΟx)]Square Wave
f(x) = (4/Ο)Ξ£ sin((2n-1)x)/(2n-1)
// Ray Optics
Waves & Optics Β· Lenses & Mirrors
THIN LENS SIMULATOR
W4
Lens
100
Object
200
40
Thin Lens Equation
1/f = 1/dβ + 1/dα΅’M = βdα΅’/dβ = hα΅’/hβ
Image
dα΅’ = βM = β
β
// Ideal Gas Law
Thermodynamics Β· PV = nRT
PARTICLE KINETICS
T1
State Variables
300 K
70%
80
Ideal Gas Law
PV = nRTKE_avg = (3/2)kT
Measured
P = βKE = β
v_rms = β
// Heat Engines
Thermodynamics Β· Carnot Cycle
CARNOT CYCLE PV DIAGRAM
T2
Reservoirs
800 K
300 K
Cycle
1.0
6.0
Carnot Efficiency
Ξ· = 1 β T_c/T_hΞ· = β%
W = Q_h β Q_c
Entropy
ΞS_total = 0 (reversible)
// Statistical Mechanics
Thermodynamics Β· Entropy & Distributions
MAXWELL-BOLTZMANN DISTRIBUTION
T3
Parameters
300 K
4 amu
1000
Maxwell-Boltzmann
f(v) = 4Ο(m/2ΟkT)^(3/2) vΒ² e^(βmvΒ²/2kT)Statistics
v_avg = βv_rms = β
v_mp = β