Fourier App vs ControlsLab

Fourier App is an interactive tool for visualizing and computing Fourier Series of piecewise functions. Define custom functions with multiple pieces and discontinuities, choose the time window, and instantly see the original signal x(t) alongside its series approximation s(t). Browse a built-in catalog with classic examples like sine, cosine, step function, rectangular, triangular, ramp, parabola, and more. View the frequency spectrum with an, bn, and cn coefficients, filter partial series terms, and explore how each harmonic contributes to the final waveform. Includes a theory section covering Fourier Series history, equations, and real-world applications such as audio streaming and noise cancellation.

ControlsLab is a professional-grade system dynamics and controls simulator designed for engineering students, educators, and practicing engineers. Simulate a mass-spring-damper system in real time. Adjust parameters with intuitive sliders and instantly see how the system responds - no coding required, no MATLAB license needed. FREE FEATURES SYSTEM SIMULATION - Mass, damping, and spring parameter control - Step, ramp, parabolic, and sinusoidal inputs - Adjustable initial conditions x(0) and dx(0) - Input signal overlay on time response plot VISUALIZATION - Live time-domain response plot - S-plane pole visualization - System stability classification - Overdamped, underdamped, critically damped detection ANALYSIS MODES - Open-loop mode: plant driven directly by input - Closed-loop mode: negative feedback with configurable setpoint PRO FEATURES - $4.99 One-time purchase, no subscription PID CONTROLLER - Full negative feedback implementation - P, PI, PD, and PID controller types - Live Kp, Ki, Kd gain tuning with instant response - Adjustable reference setpoint FREQUENCY DOMAIN - Bode plot: magnitude (dB) and phase (degrees) - Logarithmic frequency axis - Natural frequency, damping ratio, and bandwidth readouts WHO IS THIS FOR? - Undergraduate engineering students studying dynamic systems and feedback control - Graduate students reviewing control theory - Professors and educators demonstrating system behavior in lectures - Practicing engineers doing quick back-of-envelope system analysis - Anyone curious about how control systems work ControlsLab turns abstract differential equations into visual, interactive experiences. Move a slider and watch poles migrate across the S-plane. Toggle a controller and see overshoot disappear in real time. No prior programming experience required.