FUNDAMENTALS OF IMPACT AND SHOCK ISOLATION - Injury Biomechanics and Control: Optimal Protection from Impact - page 23

F

A

0 t

T

FIGURE 2.4 Exponential pulse.

is the peak magnitude of the shock force and
T is the characteristic time of the disturbance. In Examples 2.1 and 2.2, T
is the duration of the disturbance. In Example 2.3, the disturbance duration
is infinite and T is the characteristic time of the decay of the exponential
function involved in (1). In time T , the exponential function decreases by
a factor of e . As one can see from relations (2) of these examples, the peak
magnitude of the shock force can be arbitrarily large while the product

In Examples 2.1 - 2.3 | A |

T
and hence, the respective integral, remain finite. To that end, the duration
T must tend to zero as

| A |

tends to infinity. This tendency corresponds to
the characterization of shock disturbance as the imposition of a large force
for a short time.

| A |

Example 2.4 Decaying Sinusoidal Disturbance

Consider a disturbance of the form

A exp sin 2 π

T 2 t ,

t
T 1

F(t) = − 0 ≤ t< ∞ , (1)

T 1 > 0 ,T 2 > 0 .

Figure 2.5 shows the plot of this function for A > 0 . Unlike the functions
F(t) in Examples 2.1, 2.2, and 2.3, F(t) in (1) varies in sign. Specifically,
if A > 0 , then

1 )<t<T 2 n −

2 ,n =

1

F(t)> 0 f T 2 (n − 1 , 2 ,...,

F(t) < 0 f T 2 n

2 <t<T 2 n,

(2)

1

− n = 1 , 2 ,....

(continued)