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For our pure/ideal spring element, the frequency response is very easy to calculate. Let's make the input force be the sine wave/= fo sin wt, wheref0 is the amplitude in lb1 or newtons, and w is the frequency in radians per second. Recall that while all calculus operations require frequency in rad/sec, engineers often prefer cycles/sec, also called Hertz, and with symbol f. The conversion is of course f = w/2rr, one cycle/sec is 2rr radfsec. For a pure/ideal spring element, x = C.Jo sinwt, giving the graphs of Fig. 2-4. For dynamic systems in general, there will be a phase angle (phase shift) between the input sine wave and the output sine wave. For the spring element it is clear that this phase shift (called angle ¢ in this book) is zero for all values of frequency from 0 to infinity. The amplitude ratio Ax/ A1 is simply the number Cs, so it also is the same for all values of w.