Do I need to install anything?

No. It runs in any modern browser, free, with no account required.

For First Responders · Motor Driver

Motor Driver for a relay

Built for first responders planning or training for real incidents. Run fast what-if scenarios for response planning and training — no software to install in the field. Simulate a relay live below — adjust the inputs and watch it respond, right in your browser.

DC Motor

open full solver →

DC MotorLive

step response & speed-torque

Controls

Presets

Voltage (V)

Armature resistance (Ω)

Load torque (N·m)

Motor constant Kt (N·m/A)

A DC motor speeds up until back-EMF balances the applied voltage, giving a first-order step response. Its steady speed drops linearly with load along the speed-torque line: maximum speed at no load, maximum (stall) torque at zero speed. The green dot is the operating point where motor and load torque match.

▶ Run in Python

Data Inspector

No-load speed240 rad/s

Steady speed224 rad/s

Stall torque0.30 N·m

Current draw0.4 A

Reading this result: Light load: speed stays close to the no-load value, since only a small back-EMF drop is needed to supply the torque.

Governing equation

ω = \frac{V - I R}{k _{e}} = \frac{12 - 0.4 \cdot 2}{0.05} = 224 rad/s, τ = k_{t} I = 0.020 N\cdotm

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

↓

PID Control

open full solver →

PID ControllerLive

step response tuning

Controls

Presets

Proportional Kp

Integral Ki

Derivative Kd

A PID controller drives a system to its setpoint using three terms: proportional reacts to the current error, integral eliminates steady-state offset, and derivative damps overshoot. Tuning the three gains trades off speed, overshoot, and stability — the workhorse of industrial control.

▶ Run in Python

Data Inspector

Overshoot0%

Settling time0.00 s

Steady-state error0.000

Governing equation

u (t) = 4.0 e (t) + 1.00 \int e d t + 0.5 \frac{d e}{d t}

Reading this result: Balanced gains — proportional for speed, integral to remove offset, derivative to damp overshoot: the textbook well-tuned response.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

↓

Transistor Bias

open full solver →

BJT Transistor BiasLive

voltage-divider Q-point

Controls

Presets

Supply Vcc (V)

R1 (kΩ)

R2 (kΩ)

Collector Rc (kΩ)

Emitter Re (kΩ)

Current gain β

Voltage-divider bias sets a transistor's operating point (Q-point) stably against variations in β. The base voltage fixes the emitter current, and the collector-emitter voltage falls on the DC load line. For a clean amplifier, the Q-point should sit near the middle of the active region.

▶ Run in Python

Data Inspector

Collector current Ic2.52 mA

Vce8.22 V

Base voltage2.11 V

Regionactive

Governing equation

I_{C} = β I_{B} = 150 \times 0.017 = 2.52 mA

Reading this result: The Q-point sits near mid-load-line — the sweet spot for a linear amplifier, giving the largest symmetric output swing.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

↓

Bode Plot

open full solver →

Bode Plot (2nd-Order System)Live

frequency response

Controls

Presets

Natural frequency (Hz)

Damping ratio ζ

A Bode plot shows how a system responds across frequency: gain in decibels on top, phase shift below. This second-order low-pass passes low frequencies and rolls off at −40 dB/decade above its natural frequency. Low damping produces a resonant peak; high damping smooths it away.

▶ Run in Python

Data Inspector

Natural freq1,000 Hz

Damping ζ0.30

Resonant peak+4.8 dB

Roll-off−40 dB/dec

Governing equation

H (s) = \frac{ω _{n}^{2}}{s ^{2} + 2 ζ ω _{n} s + ω _{n}^{2}} = \frac{6 , 28 3 ^{2}}{s ^{2} + 3770 s + 6 , 28 3 ^{2}}

Reading this result: Low damping ζ=0.30 produces a sharp +4.8 dB resonant peak just below fn — great for selectivity, but it rings in the time domain.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

or unlock everything with Pro →

Also for:Students Researchers Educators Engineers Hobbyists & Makers K-12 Students General version →

More with Motor Driver

Motor Driver for an RLC circuit Motor Driver for a power supply Motor Driver for a transformer Motor Driver for a DC motor Motor Driver for an op-amp filter Motor Driver for an antenna Motor Driver for a transmission line Motor Driver for a PCB trace

Frequently asked questions

Is this good for first responders?: Yes — this version of "Motor Driver for a relay" is framed for first responders planning or training for real incidents. Run fast what-if scenarios for response planning and training — no software to install in the field.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.