MUJOCO · DEVICE PHYSICS

Force Balance: Spring vs Gravity

Tune the spring stiffness so the spring force balances the load's weight at the target deflection, reading force equilibrium straight off a real simulation.

01Challenge

Same device, but now the mass is right (0.5 kg) and the SPRING is wrong: stiffness 20 N/m, so the load sags all the way to -0.245 m. The spec deflection is -0.10 m. Tune the stiffness until the spring force balances gravity exactly there.

Predict firstA 0.5 kg load on a 20 N/m spring sags to −0.245 m; the spec wants −0.10 m. To lift the resting point to −0.10 m you must…

02Model

At rest, nothing moves because the forces cancel: the spring pulling up equals gravity pulling down. Spring force is stiffness times stretch; weight is m g. Set them equal at the deflection you want and solve for stiffness: stiffness equals m g over x. Half a kilo, ten centimetres of stretch, that's 0.5 times 9.81 over 0.10, about 49 newtons per metre. A softer spring sags too far; a stiffer one barely gives. The simulation just lets you watch that balance find itself.

▶ Live · scrub & hover — the mass settles exactly where spring pull equals weight — physics solves k·x = m·g live

03Guided practice

1. Solve the balance. stiffness·x = m·g → stiffness = m·g/|x| = 0.5·9.81/0.10 ≈ 49 N/m. 2. Edit the joint's stiffness="20" → 49. 3. Simulate. The load settles at -0.10 m where spring force = weight.

04Feedback

PASS WHEN PASS when the load settles at -0.10 m (±0.006): spring force balances weight there.

If your run fails, check:

Sags below -0.10 m, spring too soft; raise stiffness toward m·g/0.10 ≈ 49.
Barely deflects (above -0.10 m), spring too stiff; lower stiffness toward 49.
It oscillates and won't settle. Keep some damping (the damping term is fine at 6); the fix here is stiffness, not damping.

05Retrieve & space

Force balance: at equilibrium, spring force (stiffness·x) equals ____ (the weight m·g).
Solve: to settle a 0.5 kg load at 0.10 m on a spring, stiffness ≈ ____ N/m (49).
A stiffer spring gives a ____ deflection for the same weight (smaller).

06Mastery & project

Tune stiffness so the device settles at the spec deflection, reading force equilibrium off a real sim.

Force-balance reasoning underlies every load case your capstone device must survive.

← From CAD Body to Physics Body Reading the Verdict: Did It Settle? →

MUJOCO · DEVICE PHYSICS

Force Balance: Spring vs Gravity

Edit the MJCF device model and simulate it on real MuJoCo physics, tuning the parameter so the part settles at the spec.

You read

the body's mass, the spring and gravity forces, and its deflection each step

You change

the mass, stiffness, and damping you set on the device

Fixed

the MuJoCo solver, the device, and the settle check