Springs Demo

This demonstration plots the solution of a second order linear ordinary differential equation of the form \[mx^{\prime\prime} + cx^{\prime} + kx = F(t),\] which describes the motion of a spring.

You can initially select an example of one of the following seven types of springs:

• Free undamped
• Free underdamped
• Free critically damped
• Free overdamped
• Forced undamped
• Forced undamped - beats
• Forced undamped - resonance.

You can change the following inputs in the demonstration.

• The number \(m\) can be entered in a box.
• The number \(c\) can be entered in a box.
• The number \(k\) can be entered in a box.
• The function \(F(t)\) can be entered in a box.
• The number \(x(0)\) can be entered in a box.
• The number \(x^{\prime}(0)\) can be entered in a box.
• The interval in the \(x\)-axis on which the function is plotted can be changed by sliders.
• The interval in the \(y\)-axis which is visible can be changed by sliders.

Using this Demo

To start the demonstration, click on the button "Launch the Demonstration Now."

To change the inputs in the demonstration, note the following.

• When you type something in an input box, the demonstration won't recompute until you hit Return on your keyboard.
• When you drag a slider back and forth, the demonstration won't recompute until you let go of the mouse button.
• There may be a few second delay when the demonstration recomputes, depending on the speed of your internet connection.