I'm practicing piano for almost a year now and I'm getting very good especially at playing with both hands. But for the first time I met a piece that requires me to apply different forces on both hands. I mean I have to play the notes on my left hand "piano" and the notes of the right hand "forte" I'm finding a huge difficulty in achieving that. Anyone with exercises dedicated to this issue?
As a mature (elderly?) learner, I faced a similar difficulty about a year ago, and found these ideas helped:
With the "quiet" hand, keep the fingers as close to the keys as possible at all times (if possible, make sure that they never actually lose contact with the keys) and lift the fingers of the other hand off the keys before playing the note (loudly). It is very difficult to play really loudly with the quiet hand if you don't lift the fingers at all.
Take some VERY simple pieces, such as the first dozen pieces in Bartok's Mikrokosmos book 1, which are things like playing the same notes in both hands but an octave or two apart. Concentrate on playing one hand loudly and just touching the keys with the other hand but not actually depressing the keys. Then move on to playing loudly with one hand and pressing the keys with the other hand as softly as possible.
The thing I found difficult was making sure that the notes played by the two hands actually sounded at exactly the same time - it took me quite a lot of (very) slow practise to get the hang of it.
On this last point, I did some exercises where I played LH softly and RH loudly and deliberately playing the LH slightly before the RH note, and reversing it, so that I played the RH note slightly earlier, and then the hard bit: both exactly together.
You can focus much more easily on the dynamics by making everything else easier (and thus either automatic or requiring little attention). You could practise playing this way with a simpler piece or one you already know well.
Slowing down is also very effective — as a extreme example, if you're only pressing one note every 10 seconds is makes it exceptionally simple to focus on the force you're applying with each hand. Play as slowly as you need to get the dynamics correct, then speed up slightly. Repeat while verifying at each point that you're getting it right, backing up if you need to, until you can play full speed. (It's OK if this takes a while the first time you attempt this!)
Old John's suggestions are also excellent.
When starting to work on any technique like this, I've found it's good to isolate it down to something so incredibly simple that you are focusing only on the technique and its clarity and not at all on the happenings of a piece. You can use a very simple five finger exercises you already know very well (ex. Hanon 1), but to start, I would recommend just repeatedly playing
C-D-E-F-G-F-E-D. As with any practise, start off extremely slow.
First, play the exercise hands separate. Play the left hand forte through the exercise, then go through separately with the right hand piano. This might seem unnecessary, but it will give you a fresh feel of what each hand has to do before putting them together. Focus on the tone and dynamic of each note. Then play the exercise hands together—very slowly. Then repeat what was said in this paragraph, but with the dynamics of each hand reversed.
Once you feel comfortable start tweaking some of the variables. Increase the tempo, crescendo the right hand while decrescendoing the left in a certain amount of bars, instantly change the dynamic in one hand while maintaining a steady dynamic of the other, or flip the dynamics of each hand at the same time, etc. There are a lot of variations you can do and it can be quite fun.
From that base, you can move on to practising this in simple pieces and eventually apply it to the piece you're working on. It should be much easier at that point.
To build familiarity with this action, you may first practice a piece you already know, or just scales-- one time, focus on making one hand louder than the other, and the next time, focus on the other hand. Play as slow as you need to, to get the "feeling" correct, or at least, not as alien or hard. After that warm-up, practice the passage in which you need to apply these different "forces" slowly and gradually ramp up your speed as you become more comfortable. Remember, when you want to play things softly and with less of an accent, you should stay closer to the keyboard and slow your attack when pressing keys.
You may also find it helpful to think about the piece itself and why one hand is piano and one is forte. Most likely it is because the softer part is the harmony supporting the melody.. so I will often think about singing (internally) along with the melody, and that naturally makes the hand playing the melody louder than the other.
I'd also recommend that if you have a recording device-- even a cell phone is fine-- use it to record yourself a few times and see if you can hear the difference. Depending on the space/piano, unless we know what we're looking for, sometimes we don't "hear" correctly what is actually happening.