Learning vector quantization (LVQ): four-vectors assigned to two classes. In this, two reference vectors will be used. The following input vectors represent two classes, 1 and 2: VECTOR1 (1, 0, 0, 0), CLASS1, VECTOR2 (0, 1, 1, 0), CLASS2, VECTOR3 (0, 0, 1, 1), CLASS2, & VECTOR4 (1, l,0, 0), CLASS1. The first two vectors will be used to initialize the two reference vectors. Thus, the first output unit represents class1, the second class2 (symbolically, = 1 and = 2). This leaves vectors (0, 0, 1, 1) & (1, l,0, 0) as the training vectors. Initialize the learning rate: a = 0.1. Find new weights W2=?, & W1=?

Amass of 1.5 kg of air at 120 kpa and 24°c is contained in a gas-tight, frictionless piston-cylinder device. the air is now compressed to a final pressure of 720 kpa. during the process, heat is transferred from the air such that the temperature inside the cylinder remains constant. calculate the boundary work input during this process.

Aloaded platform of total mass 500 kg is supported by a dashpot and by a set of springs of effective stiffness 72 kn/m. it is observed that when the platform is depressed through a distance x = 12.5 cm below its equilibrium position and then released without any initial velocity; it reaches its equilibrium position in the shortest possible time without overshoot. find the position and velocity of the loaded platform 0.10 sec. after its release. if a further load of 400 kg is added to the platform, find, i) the frequency of damped vibrations, and i) the amplitude of vibration after 2 complete oscillations, given that the initial amplitude is 15 cm.

Abrake has a normal braking torque of 2.8 kip in and heat-dissipating cast-iron surfaces whose mass is 40 lbm. suppose a load is brought to rest in 8.0 s from an initial angular speed of 1600 rev/min using the normal braking torque; estimate the temperature rise of the heat dissipating surfaces.