Notes, summaries, assignments, exams, and problems for Physics

Harmonic Oscillator

In classical mechanics, a harmonic oscillator (also known as a linear oscillator or simple oscillator) is a physical system bound to a position of stable equilibrium by a restoring force proportional to the displacement from this position. A typical example of a harmonic oscillator is a mass attached to a spring. The restoring force is the elastic force F given by Hooke’s law:

F = −kx,

where x is the displacement and k is the spring constant. The motion of a body of mass m attached to the spring is governed by Newton’s second law:

[m*(d²/dt²)] * x(t) = −kx

whose general solution is:

x(t) = Acos(ωt + φ).

Here, ω = rad(k/m) is the natural oscillating frequency, A is the amplitude of the oscillation, and φ is the phase... Continue reading "Harmonic Oscillator: Definition, Applications, and Quantum Mechanics" »

If this story had been told differently, it wouldn't have mattered to anyone. The best thing about this film is the narrative. It has such an attractive and comical principle that it catches anyone. Showing the characters with insignificant details brings them closer to the ordinary mortal, so full of obsessions or supposed oddities. They and not the protagonist of the story are, in my opinion, the success of this film. Amelie is a normal character who becomes the centerpiece of a story because of her kindness. Here she appears as a modern fairy godmother, even if she replaces the magic wand with toothpaste, slippers or intentional phrases. That's why the first part of the film, where the different human stories appear, is the one I liked the... Continue reading "Amelie: A Modern Fairy Godmother and the Power of Narrative" »

Properties of Laser Light

1. Monochromaticity

Unlike discharge lamps that emit on all atomic transitions, laser emission typically corresponds to a single atomic transition of the gain medium. The spectral line width can be much smaller than the atomic transition's due to the influence of the optical cavity.

2. Coherence

Laser beams exhibit high spatial and temporal coherence.

Spatial coherence describes the regularity of the optical phase across a beam's cross-section.

Temporal coherence refers to the duration over which the beam's phase remains well-defined. The temporal coherence time (t_c) is generally the reciprocal of the spectral linewidth (ν). Consequently, the coherence length (l_c) is: l_c = ct_c = c/ν.

3. Directionality

A key characteristic... Continue reading "Properties of Laser Light: Monochromaticity, Coherence, and More" »

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What is force?

A force is a push or pull that can change the shape of an object the way that it moves. It also changes Speed and direction. You can not see. When something is moving or speeding, the force is acting.

Force arrows:

You can draw an arrow, the length of it, shows the size of force and the direction shows where is coming from.

Types:

The gravitational force, is the force that attracts you to Earth. In the earth, the force of gravity in a object is called Weight.

Electrostatic:

It acts between objects that are charged. Rubbing plastics can charge them up with electricity.

Magnetic: The magnets attract materials such as iron, steel, or nickel.

Friction:

When any object slides across a surface, the force of friction tries to stop it moving.

Fundamental Concepts in Earth Physics

Elastic Moduli and Seismic Waves

Elastic Moduli Definitions

• Young's Modulus (Y): Describes the fractional change in length of an object when subjected to a tensile stress. The formula is: Y = (F/A) / (ΔL/L₀)
• Bulk Modulus (K): Describes how a fractional change in volume depends on the applied pressure.
• Shear Modulus (G): Describes how an angle of shear depends upon a tangential stress.

Seismic Wave Types

• P-wave (Primary Wave): Characterized by compressional and expansion motion.
• S-wave (Secondary Wave): Characterized by shear motion.

Demonstration of Radiometric Age Dating

Derivation of the Decay Equation

If the decay rate is equal to $\lambda$, the probability that a given nucleus will decay in a time interval... Continue reading "Geophysical Principles: Elasticity, Magnetism, and Radiometric Dating Formulas" »

Lens

What is a real image?

An image where real rays intersect

What is a virtual image?

An image that appears to be coming from behind the mirror

Describe the law of reflection as a relationship between the angle of incidence, the angle of reflection, and the normal.

The angle of incidence, angle of reflection and normal all lie in the same plane

Describe the kinds of images that can be formed by plane mirrors.

Only virtual images, little distortion

What type of mirror produces only diverging rays?

Convex

What type of mirror can produce both converging and diverging rays?

Concave

Describe what kind of mirror you would use if you needed to view a large, spread-out area in a small mirror.

Convex

Compare the shapes of convex and concave mirrors. How are they

Key Benefits of Using Solar Power

• Clean energy
• Renewable energy

Future of Photovoltaic Systems in Industrial and Developing Countries

Does the future hold a place for photovoltaic (PV) systems in both industrial and less developed countries?

Yes, because the problem of CO2 emissions is getting bigger, and it is necessary to invest immediately in new sources of renewable energy.

Advantages of Off-Grid PV Systems for Emergency Applications

What are some advantages of using off-grid PV systems for emergency call boxes and emergency warning signals?

• They save the cost of extending power lines to far-away locations.
• In the event of an electrical failure, they will still function.

Major Disadvantage of PV Systems

PVs require light to operate. What is one big

True/False

t: A strong acid is one that will completely ionize

f: When blue litmus paper is placed in a weak acid, it will turn a darker shade of blue

f: When pH paper provides a reading which says it has a pH of 9, the substance is considered a weak acid.

f: Alpha, Beta, and Gamma are all forms of nuclear radiation that contain either positive or negative charges.

t: Fission is the process where a large nucleus splits unto two smaller nuclei.

f: The most common isotope of carbon that is used for radioactive dating is carbon-13.

t: Static friction is friction that occurs when an object is not moving.

f: When an object is accelerating but it is not traveling in a straight line, it must be moving vertically.

t: Friction is force that always opposes the... Continue reading "Science True/False and Multiple Choice Questions" »

The Scientific Method and Celestial Motion

In the Scientific Method, a hypothesis must be both testable and falsifiable. When observing the heavens, sidereal measurements are relative to the stars, while synodic measurements are relative to the Sun; for instance, the Moon is full every synodic month.

Kepler's Laws of Planetary Motion

• Kepler's 1st Law: Orbits are ellipses with two foci; the Sun is at one focus. A higher eccentricity (e) indicates a more elliptical orbit.
• Kepler's 2nd Law: The Law of Equal Areas.
• Kepler's 3rd Law: P² = a³, where P is the period in years and a is the semi-major axis in AU.

The Solar System Rotation Curve is defined by the formula v = sqrt(GM/r), where v is orbital velocity and r is the distance from the Sun.

Newtonian

Thermal Energy

Thermal energy is the average kinetic energy of the atoms or molecules in a substance.

Thermal Energy and Changes of State

When a change of state occurs, the energy transferred in heating up the substance is used to break the bonds between the molecules. The energy transferred does not increase the thermal energy but rather increases the internal energy of the substance.

Key Concepts

• The particles of a substance are in constant motion, and this increases as the substance heats up.
• Thermal energy is the average kinetic energy of the particles of a substance.
• During a change of state, the energy transferred in the heating process is used to break the bonds between molecules without increasing its thermal energy.

Temperature: Measurement