Your maximal strength and maximal oxygen uptake increase if someone encourages you, although psychologists say that this doesn't always lead to better physiological performance.
In 1996 researchers at the Auckland Institute of Technology in New Zealand published the results of an experiment in which twenty healthy students had participated. [Br J Sports Med. 1996 Sep; 30(3): 243-5.] The students were untrained. They had to overcome resistance using their biceps while the researchers measured the maximal strength that the students developed.
On one occasion the researchers didn't offer any encouragement to the students; on the other occasion they did do so. "In the set of contractions where verbal encouragement was provided, the words spoken were "Come on, you can do it", and they were repeated for the duration of the contraction", the researchers wrote. The figure below shows that the highest force measured increased by five percent as a result of words of encouragement. And yes, that was a statistically significant effect.
The figure above is from a 2002 study published in the Journal of Sports Sciences. [J Sports Sci. 2002 Apr; 20(4): 345-52.] In this study sports scientists at Bloomsburg University of Pennsylvania got 28 students to run on a treadmill for a maximal exertion test, during which the researchers measured the students' maximal oxygen uptake.
The researchers repeated the test several times, and varied the frequency with which they encouraged the students [curve with 'white' circles]. For the highest frequency – every twenty seconds – not only maximal oxygen uptake was significantly higher, but also the length of time that the students managed to keep running.
So, it would seem, encouragement not only helps strength but also endurance.
However, according to researchers at the University of Mississippi, encouragement only improves performance in people with Type-B personalities and not those with Type-A personalities. [Percept Mot Skills. 1997 Apr;84(2):507-12.]
According to the cardiologists Meyer Friedman and Mike Jordan, Type-A personalities are ambitious hardworking people with a strong sense of duty, who are therefore more likely to contract cardiovascular disease. Type-B personalities on the other hand are more relaxed people who don't work harder than is strictly necessary, and therefore suffer less from heart attacks.
According to the University of Mississippi researchers, Type-A personalities perform maximally, whether encouraged to do so or not, so words of encouragement only help people with less mental 'power'.
Br J Sports Med. 1996 Sep; 30(3): 243-5.