Carrying only the speed into a new camera path still braked: carry the spring's lead as well

type Spring = { x: number; v: number };
const CARRY_SECONDS = 0.17;
// Exact critically damped step.
function critical(s: Spring, target: number, omega: number, dt: number) {
  const e = Math.exp(-omega * dt);
  const delta = s.x - target;
  const tmp = (s.v + omega * delta) * dt;
  s.x = target + (delta + tmp) * e;
  s.v = (s.v - omega * tmp) * e;
}
// One axis; the room does the same for x, y, log distance and both lens shifts. path(u) is the walk's own curve.
// before: no carry, then the velocity alone ({ v: pose.v, lead: 0 }); the new path starts at the pose either way.
let carry = { t0: 0, v: 0, lead: 0 };
function startPath(pose: Spring, goal: number, now: number) {
  carry = { t0: now, v: pose.v, lead: goal - pose.x };
}
function goalAt(pathValue: number, now: number) {
  const tau = Math.max(0, now - carry.t0) / 1000;
  const e = Math.exp(-tau / CARRY_SECONDS);
  return pathValue + carry.v * tau * e + carry.lead * e; // at tau = 0 the goal has not moved at all
}
// each frame: critical(pose, goalAt(path(u), now), 34, dt), where path: (u: number) => number