In the lab you will implement a fourth order Butterworth filter with a cutoff frequency of 1 kHz, and a gain of 4.0. From the tables in reference 1, the appropriate transfer function is

On solidification from a melt, the polymer polyethylene forms a semi-crystalline spherulite structure. (i) sketch an individual spherulite and label the amorphous and crystalline regions. (ii) draw a schematic to show the changes in specific volume with temperature during cooling from the melt, comparing it to the theoretical extremes of fully crystalline and fully amorphous (indicate tm and tg)