FUNDAMENTALS OF IMPACT AND SHOCK ISOLATION - Injury Biomechanics and Control: Optimal Protection from Impact - page 22

Example 2.2 Half-Sine Pulse

The half-sine pulse is defined as

⎧
⎨

A sin πt
T

if 0 ≤ t ≤ T,

F(t) = (1)

⎩

if t > T. 0

The function of (1) is shown in Fig. 2.3 for A > 0 . The integral of Eq.
(2.9) for function (1) is
∞

T

2 | A | T

| F(t) | dt = | F(t) | dt = . (2)

π

0 0

F

A

t

0 T

FIGURE 2.3 Half-sine pulse.

Example 2.3 Exponential Pulse

Define the exponential pulse as

T t exp T

,

A − t

F(t) = 0 ≤ t< ∞ , T > 0 , (1)

T

where A and T are specified constants. The function F(t) is shown
in Fig. 2.4 for A > 0 . Unlike the rectangular and half-sine pulses, the
exponential pulse does not vanish for any t > 0 . The integral of Eq. (2.9)
for function (1) is

∞

| F(t) | dt =| A | T exp ( 1 ). (2)

0