HOOKE'S LAW Introduction In physics, Hooke's Law is one of the fundamental principles governing how objects deform under external forces . Named after the 17th-century British physicist Robert Hooke, this law provides a crucial understanding of the behavior of elastic materials, such as springs and rubber bands. Whether stretching a rubber band or compressing a spring, Hooke's Law helps explain what happens when forces act on these materials. What is Hooke's Law: Hooke's Law states that the force F needed to extend or compress a spring by some distance x is proportional to that distance. Mathematically, it is expressed as: F= -kx Here k represents the spring constant, which is the measure of the stiffness of the spring, and x is the displacement from the displacement position. The negative sign indicates that the force exerted by the spring is in the opposite direction of the displacement. Understanding the Spring Constant: The spring constant k is a critical co...
PROBABILITY AND RANDOM SIGNALS INTRODUCTION TO PROBABLITY: Probability is a number that describes a set. ▪ The higher the number, the more probability there is. ▪ In this sense probability is like a quantity that measures a physical phenomenon ▪ Methods used for assigning probabilities ▪ Personal Approach ▪ Relative Frequency Approach ▪ Classical Approach ▪ Study of probability refers to an experiment consisting of a procedure and observations. ▪ In random variables, each observation corresponds to one or more numbers. ▪ In stochastic processes, each observation corresponds to a function of time. ▪ The word stochastic means random. ▪ In stochastic /random processes, we study random functions of time. ▪ Almost all practical applications of probability involve multiple observations taken over a period of time. SET THEORY: Set theory is the mathematical theory of well-determined collections, called sets, of objects that are called members, or elements, of the set. • Set Theory is a b...