Most of your small-engine equipment (think lawnmower, weed whacker, leaf blower) are typically equipped with what's called a recoil starter which is a rope and pull handle which you tug in a starting ritual that becomes personal as the equipment ages and the user adapts to various idiosyncratic choke and primer bulb rythms. Inevitably, either the starter rope or the recoil spring will fail. These are cheap (e.g. the rope costs about a buck) repairs the handyman can do himself with a little effort and patience. Always wear safety goggles for this work since a mishap with a spring under tension can easily result in blindness. Usually, if the rope or spring has failed, all tension will have dissipated, but never assume it for safety's sake. The common indicator of a broken spring is a rope that only partially recoils back into the winder. If you are vigilant about maintenance and are replacing a frayed rope before it fails, untie the knot in the handle so you can release the rope and dissipate the preload on the spring while still having the full length of the original rope as your measuring guide for the replacement rope. Alternatively, cut the rope and simply use both pieces combined as your reference length. Once there is zero preload on the spring, you ought to be able to lift the winder right off of the spring and tensioning cup without the spring uncoiling. If there is preload, lifting the winder will pull the center of the spring with it and it will uncoil fiercely with all the tension contained in the tensioning cup (you're wearing goggles, right?). Understand that the free spring will never fit inside the tensioning cup. It must be coiled under tension to reduce its outer diameter down to the size of the tensioning cup. If the spring jumps out of the tensioning cup or you intentionally take it out to clean or replace it, take note of the direction it lays since it is possible to install them backwards.
Remeber to preload the spring a little by rotating the winder in the direction simulating a rope pull but without letting any rope off the spool and then feeding it through the grommet and tying it off in the pull handle (you've done it right if it draws all the slack back in when you let it go). You don't want to put too much preload or it just makes it harder to pull the rope and you may end up breaking the spring, especially if you reach its limit of travel at full rope extension. When servicing the recoil starter, I like to clean the spring and spray with WD-40 for a good balance of minimizing rust, lubricating, and not attracting too much dirt. It is also possible to use motor oil or bearing grease. I don't recommend installing the spring dry because it will rust and fail sooner. Springs come in different sizes and strengths, so you're best bet is to source a replacement from a vendor that deals with your make (Briggs, Homelite, etc). There isn't anything magical about the rope, but you must get a top-quality variety that won't rot with UV exposure. Let your spring-time gardening and lawn maintenance resume.