Spring-Mass System

Simulation Information

This simulation consists of an object attached to a spring that can stretch and contract.

You can control the simulation using these variables:

• Mass: The mass of the object
• Initial Position: The initial displacement of the object relative to the point of equilibrium
• Stiffness: The stiffness coefficient of the spring

The simulation also contains these output measurements:

• Time: The time that has passed
• Period: The period of the spring-mass system
• Amplitude: The maximum displacement of the object relative to the point of equilibrium
• Position: The current displacement of the object relative to the point of equilibrium
• Velocity: The current velocity of the object
• Force: The force currently being exerted on the object by the spring
• Acceleration: The current acceleration of the object

Controls:

• Use the start and stop buttons to start and stop the simulation
• Use the step button to advance the simulation by 0.01 seconds
• Use the reset button to restore the simulation to its initial state

Equations:

• \( T = { 2 \cdot \pi \cdot \sqrt{ m \over k } } \)
  • \(T\) is the period of the spring-mass system
  • \(m\) is the mass of the object
  • \(k\) is the stiffness coefficient of the spring
• \( x = { x_0 \cdot cos{ t \cdot k \over m } } \)
  • \(x\) is the displacement of the object relative to the point of equilibrium
  • \(x_0\) is the initial displacement of the object relative to the point of equilibrium
  • \(t\) is the time that has passed
  • \(k\) is the stiffness coefficient of the spring
  • \(m\) is the mass of the object
• \( v = { -2 \cdot \pi \cdot x_0 \cdot sin{ t \cdot k \over m } } \)
  • \(v\) is the velocity of the object
  • \(x_0\) is the initial displacement of the object relative to the point of equilibrium
  • \(t\) is the time that has passed
  • \(k\) is the stiffness coefficient of the spring
  • \(m\) is the mass of the object
• \( F_s = { -k \cdot x } \)
  • \(F\) is the force exerted on the object by the spring
  • \(k\) is the stiffness coefficient of the spring
  • \(x\) is the displacement of the object relative to the point of equilibrium

Notes:

• The dotted line represents the point of equilibrium.