Aircraft very rarely take off at full power. The redution in power can be a 'de-rate' of the engine, (telling the performance software the engine has less power (or in some cases that it's a different version of the engine with less power), or it can be with an 'assumed' temperature where a different outside air temperature is uded to acheive the thrust reduction. The benefit of this is that engine life is prolonged and savings are made. It sounds daft at first, but a good analogy is if you think when you accelerte your car, you could use full accelerator but probably don't to preserve the life of the engine.
The parameters which determine how much power reduction is safe are runway length, tempearture, wind, air pressure and runway condition (i.e wet or icy) and condition of the aircraft - some failures (a brake unit for example) can still allow a takeoff to be made. Bahrein for example has a very long runway, so quite a big reduction can be made which is what you have experienced. The maximum power reduction allowed by licensing authorities is 25%.
The calculations are done either from a book of tables or graphs, or from the aircraft's own flight management computer software, or in my airline's case, from a datalink to company headquaters. Interestingly, the Airbus (for all it's complexity) doesn't have the take off performance built in. Boeings tend to (depending on the customer's requirements) but it wasn't permitted to use it by our licenscing authority on the one Boeing type I used to fly.
I should mention that it's perfectly safe. The calculation assumes that if an engine fails on take off, the remaining good engine can safely get the aircraft airborne with the reuduced power. The pilot of course has the option of using full power for increased safety.
The 'shiver' on take off could be one of two things. Immediately on take off, a small thump is felt as the oleos (the aircraft's suspension which are built into the gear legs and is based on compressing oil and gas, a bit like a shock absorber on a car) reach their extension limits. Also, the wheels are braked as you don't want a fast rotaing heavy wheel spinning when it's retracted ito it's wheel well. The mainwheels have the main brakes to stop them, but there is no brake on the nosewheel. So when it retracts, it rubs on a brakepad attached to the top of the wheel well. It is probably this rubbing (which lasts for several seconds) which you can sense.