Notes, summaries, assignments, exams, and exercises for Physics for University

interest of the Fourier transform
• Electronics
• Signal Theory
• Telecommunications
• Optics
• Acoustics
• Radar
• Image processing
convolution product of discrete FFT (Fast FourierTransform) => time ? N log N
-Needed a FFTper each of the two images on which you must do the convolution product. And antitransformadaa the acabarde make the product. In total, we need 3 Fast Fourier transform.
• Image Space => time NN ?
space filtering of specific frequencies freqüè preferences eliminacióde
• Periodic measurement of elements
• We will say that two vectors, orthogonal vectors are orthogonal if their inner product is zero: (u, v) = 0
• The domestic product, in this case is defined as
?Uv = 0
domestic

Material Testing: Hardness, Toughness, Fatigue, and Creep

Hardness Testing

Static Methods

• Brinell: A steel ball indenter is used, and the area of the footprint is measured. Suitable for metals.
• Vickers: Employs a pyramidal indenter tip with a square base. The surface of the print is measured. Prints are comparable regardless of the load. Applicable to any material (soft or hard), and thin pieces can be measured with small loads. Surface hardness can also be measured.
• Rockwell: Uses either a steel ball (Rockwell B) or a diamond cone (Rockwell C) penetrator. Measures the depth of the trace. Offers universal application and direct reading.

Dynamic Methods

• Poldi Method
• Rebound (Shore or Hammer Scleroscope)

Toughness Testing

Toughness is the work or energy...

Newton's Rings are concentric circular bright and dark rings formed due to interference between light waves reflected from the upper and lower surfaces of a thin air film.

Theory of Newton's Rings

When monochromatic light falls on the thin air film formed between the plano-convex lens and a glass plate, two reflected rays are produced:

• One from the upper surface of the air film.
• Another from the lower surface of the air film.

These reflected rays interfere with each other:

• Constructive interference produces bright rings.
• Destructive interference produces dark rings.

Thus, alternate bright and dark concentric circular rings are formed.

Determination of Refractive Index of a Liquid

When a liquid is introduced between the lens and the glass plate, the...

Bertrand Russell (1872–1970)

Bertrand Russell lived from May 18, 1872, to February 2, 1970. He was renowned as a philosopher, famous for his 1905 essay "On Denoting". As a mathematician, he co-authored the three-volume Principia Mathematica with Alfred North Whitehead. He was also a Nobel Prize winner, receiving the 1950 Nobel Prize in Literature. Notably, he is not the origin of the "Turtles all the way down" story.

Aristotle (384–322 BC)

Aristotle was a Greek philosopher who lived from 384 to 322 BC. He founded the Peripatetic School of Philosophy around 335 BC. He is widely known as the "Father of Western Philosophy" and significantly influenced both Christian and Islamic thought.

Ptolemy (c. AD 100–170)

Claudius Ptolemaeus, also known...

Planetary Systems and the Solar System

A planetary system is a set of gravitationally bound non-stellar objects in orbit around a star. A planet is a non-stellar object in orbit around a star. The barycenter is the center of mass of two or more bodies orbiting each other.

The Eight Planets and Other Bodies

The solar system consists of eight planets, their moons, asteroids, comets, and other minor bodies. The eight planets are:

• Mercury
• Venus
• Earth
• Mars
• Jupiter
• Saturn
• Uranus
• Neptune

Only five of these planets are visible to the naked eye. Pluto is classified as a dwarf planet or planetoid.

The Solar System Structure

The Solar System is the gravitationally bound system comprising the Sun and the objects that orbit it, either directly or indirectly. Of those...

Understanding Hooke's Law

Hooke's Law states that the deformation of an object is proportional to the force applied. When one magnitude or signal is proportional to another, a relationship can be established between both magnitudes by multiplying one of them by a coefficient of proportionality.

In this case, the force applied (F) is proportional to the elongation (x) of a spring. This relationship is expressed as:

F = kx

Where k is the coefficient of proportionality, known as the spring constant. Its value is defined as:

k = F / x

Units and Elastic Characteristics

In the International System of Units (SI), the spring constant is measured in N/m. This constant is a characteristic of the spring's stiffness:

• Hard springs: Have a high k value.
• Lazy (soft)

Fundamental Concepts and Assumptions

Temperature is a physical quantity whose value is an index of the degree of molecular kinetic energy.

Temperature Scales

Temperature scales are based on two fixed points:

• The conventional temperature scale.
• The absolute temperature scale (Kelvin, °K).

First Postulate: Temperature and Thermal Gradient

Temperature is a scalar quantity that, at each point, is a function of its position coordinates and time.

Defining the Thermal Gradient

If we consider a stationary field, we can define the gradient of $T$ at each point as a vector given by the expression:

This vector gives us the thermal gradient at each point of the field.

Statement of the First Postulate

The First Postulate states: "Heat is a form of energy exchange

Control System Specifications

1. Steady-State Value: The final value of the step response, or the steady-state error (the difference between the reference and output signal after the transient response).
2. Rise Time: The time elapsed up to the instant at which the step response reaches, for the first time, the value K*Y. The constant K varies from author to author, being usually either 0.9 (overdamped) or 1 (underdamped).
3. Overshoot, M: The maximum instantaneous amount by which the step response exceeds its final value. It is usually expressed as a percentage of Y.
4. Undershoot, M: The (absolute value of the) maximum instantaneous amount by which the step response falls below zero.
5. Settling Time, T: The time elapsed until the step response enters (without

Geographic Positioning

Single-station RTK uses the GPS satellites in combination with a GPS transmitter installed at a known reference position, whereas network RTK operates with GPS satellites in combination with multiple reference stations. With a collation of reference stations covering a region, they provide spatially varying compensation regarding atmospheric sources of positional error, such as ionic activity and electric conductivity. SWEPOS is the national Swedish network of positional reference stations.

At Least Two Different Types of Sensors

Passive sensors utilize the reflectance of external energy sources (like the Sun) or blackbody radiation, whereas active sensors utilize the reflectance of a signal emitted by the sensor system...