Can anybody give me the hint where to start on this question?

 

Two simple harmonic oscillators of the same frequency and in the same direction having amplitudes 5 mm and 3 mm, respectively and the phase of the second component relative to the first is 30°, are superimposed. Find the amplitude of the resultant oscillation and its phase relative to the first component.

The first thing I´d try to do is looking "superimposed" up in a dictionary but assuming you´re either a native english speaker or translated that term from your native language, you might skip that step.

 

Having looked it up and it being what I assumed I´d say start by asking yourself what the total deviation is when the deviation of osci 1 is x and the deviation of osci 2 is y. Aswering this question gives you the "resultant oscillation".

Can anybody give me the hint where to start on this question?

 

Yes, write down a sinusoidal function to describe each oscillator and add them up.