Wahadło Sprężynowe: Energy Transformations and Motion

This page provides a detailed illustration of a wahadło sprężynowe (spring pendulum) and its energy states throughout its oscillatory motion. The diagram shows the pendulum at various points in its swing, highlighting the changes in energy and forces acting upon it.

Definition: A spring pendulum is a mass attached to a spring that oscillates vertically, converting between potential and kinetic energy.

The illustration demonstrates how the przemiany energii w ruchu wahadła sprężynowego occur as it moves through different positions:

1. At the equilibrium position:

   • Kinetic energy (Ek) is at its maximum
   • Gravitational potential energy (Epg) and spring potential energy (Eps) are equal
   • The net force (FN) is zero

2. At the highest point:

   • Gravitational potential energy (Epg) is at its maximum
   • Kinetic energy (Ek) is zero
   • Spring force (Fps) is at its minimum

3. At the lowest point:

   • Spring potential energy (Eps) is at its maximum
   • Kinetic energy (Ek) is zero
   • Gravitational force (Fg) is at its maximum

Highlight: The total mechanical energy of the spring pendulum remains constant throughout its motion, in accordance with the zasada zachowania energii (law of conservation of energy).

The diagram also includes important formulas related to the spring pendulum:

Vocabulary:

• Epg = mgh (gravitational potential energy)
• Eps = ½kx² (spring potential energy)
• Ek = ½mv² (kinetic energy)
• T = 2π√(m/k) (okres drgań wahadła sprężynowego wzór - period of oscillation)

These equations help in understanding the badanie wahadła sprężynowego and its behavior. The period of oscillation (T) depends on the mass (m) of the bob and the spring constant (k), which is crucial for determining the częstotliwość drgań wzór (frequency of oscillation).

Example: As the mass (m) increases, the period of oscillation (T) also increases, meaning the pendulum swings more slowly.

The page concludes with notes on how different factors affect the pendulum's motion:

• Increasing kinetic energy (Ek) results in faster motion
• Higher gravitational potential energy (Epg) corresponds to a higher position of the weight
• Greater spring potential energy (Eps) indicates a more stretched spring

This comprehensive overview provides a solid foundation for understanding the przemiany energii w ruchu drgającym zadania (energy transformations in oscillatory motion problems) and the fundamental principles governing the behavior of spring pendulums.