330 JOURNAL OF COSMETIC SCIENCE BACKGROUND SIMPLE HARMONIC MOTION Simple harmonic motion is the type of motion that occurs when an object at rest is displaced by a force and the object tries to restore itself to its resting position. Figure 1 displays three examples of simple harmonic motion-a simple pendulum, a vertical spring, and a torsion pendulum. Simple harmonic motion has a specific frequency. The period (time for one oscillation cycle) remains constant even though the amplitude of the oscillation decays. In the case of a torsion pendulum, the period can provide information about the torsional rigidity of the sample connecting the pendulum to the vertical support. TORSIONAL SHEAR OF FIBERS IS GREATEST AT THE PERIPHERY The surface of a fiber to which torque is applied has the maximum influence on the shear modulus determination. For hair fibers, the surface consists of the cuticle layer. Figure 2 is a diagram showing a cylinder to which torque is applied. Torsion generates varying levels of shear within the cylinder as a function of distance from the center. In Figure 2, a gray square is shown in (a) before torque is applied while (b) and (c) show the effects of shear on the gray square after torque is applied. The wedge on the top of the cylinder in Figure 2 (c) shows the diminishing shear towards the center of the cylinder. The shear stress will be r0, where r is the distance from the center. At the fiber surface it will be R0, R being the radius of the fiber. At the center the shear stress will be 0 (r = 0). EXPERIMENT AL MEASUREMENT OF SHEAR MODULUS Measurement of shear modulus of single hair fibers using the single fiber torsion pen- dulum have been discussed in derail in an earlier communication (1). For humidity dependent shear modulus measurements the hair fiber mounted on the pendulum was surrounded by a small humidity chamber. The relative humidity was changed by 10% intervals using wet and dry nitrogen (±1-2% RH). Simple Pendulum Vertical Spring Torsion Pendulum Figure 1. Examples of simple harmonic motion.

2006 TRI/PRINCETON CONFERENCE Figure 2. Torsional shear of a cylinder. = . .,. . .... .,,..,.,.,,..,. .. ""'", .,�..,_,......,. ,. . .,.. ,,,__, .,.,.,.. . .. ....,,,.,...,,.y.,,,.,.,.. .,,.,..,,.�., ,,, ... ,,, ... , -�-.,,,,,,,,.,...,.__,. , .,,..,,.,., ,. ' I Oneway Analysis of Shear Modulus By_Treatment________ -···-------··-,,··-··--·--··· (/) :::I 1.2....------------------....-----------, 1.1 -g 0.9 0 ffi 0.8 en 0. 7 0 0.6 0.5 ........ ---------.---------........---------J Control Treatment t Means Comparisons Decuticled Each Pair Student's t 0.05 i Comparisons for each pair using Student's t Level Control A Decuticled Mean 0.99676000 B 0.62470000 Levels not connected by same letter are significantly different. Figure 3. Effect of cuticle abrasion on shear modulus. 331 The shear modulus (G) of the fiber was calculated by the following equation, assuming an elliptical cross section. lfrrrLM G =------ T 2 (a3b + ab3)