The equation of harmonic oscillations registers taking into account knowledge of a type of fluctuations, the number of various harmonics. It is also necessary to know such integral parameters of fluctuation as a phase and amplitude.
Instruction
1. It is known that the concept of harmony is similar to a concept of a sinusoidalnost or a kosinusoidalnost. It means that it is possible to call harmonic oscillations sinusoidal or cosinusoidal depending on an initial phase. Thus, writing down the equation of harmonic oscillations, first of all function of a sine or cosine registers.
2. Remember that trigonometrical function of a sine at its standard record has the maximum value equal to unit, and the corresponding minimum value differing only he is familiar. Thus, amplitude of fluctuations of function of a sine or cosine is equal to unit. If before a sine to deliver some coefficient as proportionality coefficient, then amplitude of fluctuations will be equal to this coefficient.
3. Do not forget about that, as in any trigonometrical function there is an argument describing such important parameters of fluctuations as an initial phase and frequency of fluctuations. So, any argument of some function comprises some expression which, in turn, contains some variable. If it is about harmonic oscillations, then expression is understood as the linear combination consisting of two members. Time size serves as variable. The first member is the work of frequency of fluctuations and time, the second – an initial phase.
4. Sort out how influences a type of fluctuations of value of a phase and frequency. Draw function of a sine in which argument there is a variable without coefficient on the sheet of paper. Nearby draw the schedule of the same function, but before an argument deliver the proportionality coefficient equal to ten. You will see that at increase in the coefficient of proportionality facing a variable the number of fluctuations increases by the fixed time interval, that is frequency increases.
5. Represent standard function of a sine on graphics. In same the graph show as the function differing from previous in presence of the second member in an argument, to equal 90 degrees will iron. You will find out that the second function will actually represent function of a cosine. As a matter of fact, such conclusion is not surprising if to use formulas of reduction of trigonometry. So, the second member in an argument of trigonometrical function of harmonic oscillations characterizes the moment with which fluctuations begin therefore it also is called an initial phase.