I have to work out with a injured rotator cuff and Osgood's slaughter.?

The Osgood-Schlater's disease is easier to work with. A lot depends upon where you are working out. In a gym it will be easier to do depending upon the equipment available. What you are looking for is a range limiting device on the piece of equipment. So for knee extension movements set the device for 30 degrees and lift from that point up. Keep the resistance light and the speed of the movement very slow. Each contraction should take you ten seconds in each direction. That forces the weight or resistance factor to be very light. Only one set will be necessary for each movement. You will build strength and keep the muscle toned. If you are lifting at home then do these two exercises. Get a large can of tomato juice or other product that you can use. Cover the can with a large towel. Place one leg on the can with the knee being on top of the can. Place an ankle weight across the ankle and slowly lift the lower leg up. Do this in sets of fifteen. Start with one or two pounds and work your way up. Starting from a long sitting position keep the knee absolutely straight. Using an ankle weight around the ankle lift up the leg from the hip. Lift the leg up until the calf just clears the floor. Return the leg to the floor. This can be done as much as you like and again work the resistance factor up slowly. As for the rotator cuff you have not stated what injury you have. The most likely is the supraspinatus. Try these movements but here the weight factor cannot be above one pound until a definite diagnosis can be provided. Going above that weight is only asking for problems. To do this movement stand up straight or sit up straight. Have the arm hang down at the side and slowly bring it up at a 45 degree angle from the body. The hand position is having the thumb down so you are lifting the weight from the bottom and having it move up. This movement is done very slowly at about ten seconds in each direction. Only one set is needed. The next movements are done lying down on the side with a pillow between the ribs and the elbow. Hold a weight while the forearm is across the stomach. Lift the arm up by rotating the shoulder until the forearm is perpendicular to the floor. Do this in sets of ten. Do no more than three. The next movement is done on the opposite side with the arm lying on the floor. Curl the weight up across the body by rotating the shoulder. Again do three sets of ten repetitions.