String length

We see that the time interval during which the mass moves from the original position and back to the same place, T, is proportional to the string length and becomes smaller with an increase of the gravitational field. The constants A and B are defined only by the initial conditions. For example, if at the instant t = 0, we have... 

Assuming that an error of measuring the string length is zero, it is simple to obtain a relation between the accuracy dT of a period and dg of the gravitational field. As follows from Equation (3.30)... 

Thus, in general the pendulum moves along an ellipse on the spherical surface with radius equal to the string length, /. This motion has a periodic character and the period is that of the swinging, T — Injco). In particular, if the initial conditions are... 

In practice, of course, the string length is finite, and the limits of integration are from the x coordinate of the left endpoint to that of the right endpoint, e.g., 0 to L. 

Figure 7.13 Wave motion in restricted systems. A, In a musical analogy to electron waves, one half-wavelength (X/2) is the quantum of the guitar string s vibration. The string length L is fixed, so the only allowed vibrations occur when /. is a whole-number multiple (n) of X/2. B, If an electron occupies a circular orbit, only whole numbers of wavelengths are allowed (n = 3 and n = 5 are shown). A wave with a fractional number of wavelengths (such as n = 3g) is forbidden because it rapidly dies out through overlap of crests and troughs.

PRINT Maximum string length found is P 7800 STOP... 

Binary coding for a parameter is done as follows. Suppose we have a rate coefficient = 9.08 X 10 then if we write that rate coefficient as 10 , with —10 < P < 10, a binary coding with string length of 16 bits is given by... 

---