Casos: 

• Collisions and Conservation of Momentum

• Single Spring

• Double Spring 1D

• Double Spring 2D

• Simple pendulum

• Double Pendulum

• Chaotic pendulum

• Pendulum+Cart

• Molecule with 3 atoms

• Molecule with 6 atoms

• Roller coaster simple

• Roller coaster with spring

• Roller coaster with flight

• Roller coaster with 2 Balls

• Dangle Stick

In this simulation you can drag either block. Try changing the mass of the blocks to see if the collisions happen correctly. The spring and block on the left use the same model as the single spring simulation. For a collision with the wall, we simply reverse the velocity. For collisions between moving blocks we use the law of conservation of momentum to determine the new velocities.

• What is the relationship between acceleration and position?
• How do mass or spring stiffness affect the relationship between acceleration and position?
• How do mass or spring stiffness affect the period or frequency of the oscillation?

If you've ever played with an oscilloscope you've probably seen curves like these. They are called Lissajous curves and occur because the behavior is generated by simple sine and cosine functions.

Creat per  Erik Neumann.

An immoveable (but draggable) anchor point has two spring and bobs hanging below and swinging in two dimensions. We regard the bobs as point masses. We label the upper spring and bob as number 1, the lower spring and bob as number 2. 

• What is the relationship between angular acceleration and angle?
• How do mass, length, or gravity affect the relationship between angular acceleration and angle?
• For small oscillations, how do length or gravity affect the period or frequency of the oscillation?

For small angles, a pendulum behaves like a linear system (see Simple Pendulum). When the angles are small in the Double Pendulum, the system behaves like the linear Double Spring. For large angles, the pendulum is non-linear and the phase graph becomes much more complex. You can see this by dragging one of the masses to a larger angle and letting go.

A damped driven pendulum is often used as a basic example of a chaotic system. For a chaotic system the future behavior is highly dependent on the exact value of the initial conditions. A tiny change in initial conditions can cause huge changes after a short period of time. Not all combinations of the parameters (eg. length, gravity, drive amplitude, drive frequency, damping,...) will lead to chaos. Many combinations result in simpler repeating behavior. While you can't predict the exact state of the system at a given time in the future, it is possible to show that the system will follow an elaborate pattern, These patterns are fractals, which are patterns that repeat themselves when you magnify them.

In this system there is a wheeled cart moving along a horizontal track. From the cart a pendulum is suspended. A spring is attached to the cart as shown. There are two ways to find the equations of motion for a system like this, the direct Newtonian way or the indirect Lagrangian way. We show both methods here.

Creat per  Erik Neumann.

We have a massless rigid stick with a point mass on each end. One end of the stick is attached to a spring, and gravity acts.

It is an Molecule with three differents atoms; drag an atom with your mouse; change a parameter by clicking on it, typing, and hit enter.

It is an Molecule with six differents atoms; drag an atom with your mouse; change a parameter by clicking on it, typing, and hit enter.

Try dragging the ball to a certain height on a curve, and letting go. If damping (friction) is set to 0, the ball should reach the same height on the track again and again. It shouldn't gain or lose height at the moment that it reverses direction. At that moment the velocity is zero, and all the energy is gravitational (potential) energy.

If you had first-year physics in college, you probably solved lots of problems with a ball rolling down a flat inclined plane. Did you ever wonder how to solve for the motion with a curved surface instead?
Of course the same principles apply, but the forces are changing as the slope changes. So the math gets a bit more interesting.

This version of the roller coaster has the ball jump off the track when appropriate. When the ball is on the track, it is colored blue; when in free flight it is colored red.

This simulation is a variation of the Roller Coaster with Spring The difference here is that the other end of the spring is attached to another ball on the track, instead of being fixed.