Planetary Movement | Periodic Motion| Oscillation Flashcards
was a German astronomer, mathematician, and key figure in the scientific revolution. Kepler is best known for formulating the three laws of planetary motion, which fundamentally changed our understanding of the solar system and laid the groundwork for classical physics.
Johannes Kepler (1571–1630)
“The orbit of a planet around the Sun is an ellipse, with the Sun located at one of the two foci.”
Rather than moving in a perfect circle, planets follow elliptical orbits. This means they are sometimes closer to and sometimes farther from the Sun. The Sun occupies one of the two focal points of this ellipse, making planetary orbits slightly “stretched”.
Law of ellipses
“A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.”
When a planet is closer to the Sun, it moves faster in its orbit; when it’s farther, it moves more slowly. This is because the imaginary line connecting the planet and the Sun sweeps out equal areas over equal times. This law implies that planets do not travel at a constant speed in their orbits.
Law of equal areas
“The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit”
The farther a planet is from the sun, the longer it takes to orbit it, in a predictable relationship.
Law of harmonies
A motion that repeats itself after equal intervals of time is known as
Periodic motion
Objects in periodic motion follow a predictable path, returning to a specific position after a fixed duration, known as the
Period
This is a special type of periodic motion where the restoring force is directly proportional to the displacement from an equilibrium position.
Simple Harmonic Motion (SHM)
Motion along a straight line that repeats (e.g., spring-mass system).
Linear periodic motion
is a back-and-forth motion is repeated at a fixed time interval around and equilibrium position.
Oscillation
A more common term for oscillation is
Vibration
Occurs when an external periodic force drives the system. The system oscillates at the frequency of the applied force rather than its own frequency.
Forced oscillation
A special case of forced oscillation that occurs when the frequency of the external force matches the system’s natural frequency. The amplitude of oscillation becomes very large, often limited only by damping.
Resonant oscillation
is the specific frequency at which a system naturally oscillates when it is displaced from its equilibrium position and then allowed to vibrate freely without any external forces acting on it (other than those that initially set it in motion).
Natural frequency
Occur when a system oscillates at its natural frequency without any external force acting on it. The amplitude remains constant (in the absence of damping).
Free oscillation
The amplitude of oscillation decreases over time due to energy loss, usually from friction or air resistance. Damped oscillations can be further classified as underdamped, critically damped, or overdamped depending on how quickly the oscillations decay.
Damped oscillation
A critically damped system is one where the damping force is just strong enough to return the system to equilibrium as quickly as possible without oscillating. In other words, in critical damping, the system does not overshoot its equilibrium position, nor does it oscillate back and forth before settling.
Critically damped
An underdamped system is one in which the damping force is relatively weak, allowing the system to oscillate around its equilibrium position with a gradually decreasing amplitude
Undamped
An overdamped system is one in which the damping force is so strong that it prevents oscillations entirely. Instead of oscillating around the equilibrium point, the system returns to equilibrium very slowly, without ever crossing over or oscillating around it.
Over damped
