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### 1.2.1 Defining a function

Consider a damped sine wave. It describes the time evolution of an oscillator, such as a weight on a spring, which bobs up and down for a while after you whack it. The basic shape of the wave is determined by the Q of the oscillator; a high Q means there is little friction, and the weight will continue bobbing for many cycles, while a low Q means a lot of friction and few cycles. The amplitude of the oscillation is therefore a function of two parameters -- the phase (time in units of the natural period of the oscillator), and the Q:

 ```func damped_wave(phase, Q) { nu = 0.5/Q; omega = sqrt(1.-nu*nu); return sin(omega*phase)*exp(-nu*phase); } ```

Within a function body, I terminate every Yorick statement with a semicolon (see section 1.1.1 Defining a variable).

The variables phase and Q are called the parameters of the function. They and the variables nu and omega defined in the first two lines of the function body are local to the function. That is, calling damped_wave will not change the values of any variables named phase, Q, nu, or omega in the calling environment.

In fact, the only effect of calling damped_wave is to return its result, which is accomplished by the return statement in the third line of the body. That is, calling damped_wave has no side effects. You can use damped_wave in expressions like this:

 ```> damped_wave(1.5, 3) 0.775523 > damped_wave([.5,1,1.5,2,2.5], 3) [0.435436,0.705823,0.775523,0.659625,0.41276] > q5 = damped_wave(theta,5) > fma; plg, damped_wave(theta,3), theta > plg, damped_wave(theta,1), theta ```

The last two lines graphically compare Q=3 oscillations to Q=1 oscillations.

Notice that the arguments to damped_wave may be arrays. In this case the result will be the array of results for each element of input; hence q5 will be an array of 200 numbers. Nor is Yorick confused by the fact that the phase argument (theta) is an array, while the Q argument (5) is a scalar. The precise rules for "conformability" between two arrays will be described later (see section 2.6 Broadcasting and conformability); usually you get what you expected.

In this case, as Yorick evaluates damped_wave, nu and omega will both be scalars, since Q is a scalar. On the other hand, omega*phase and nu*phase become arrays, since phase is an array. Whenever an operand is an array, an arithmetic operation produces an array as its result.