Physics of Oscillations
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Free Oscillations of a Linear Torsion Pendulum

(A Virtual Lab for Undergraduate Students)

A computer model of a mechanical linear oscillator is presented on this page. The Java-applet requires some time to load, so please be patient while it is starting. After the applet loaded, you can switch to off-line mode.

Java applets are run by web browsers (with Java plugin installed) under security restrictions to protect the user. In case you have Java 7 or Java 8 installed on your machine, trying to run Java applications generates a message:

  • Java applications blocked by your security settings.
As a workaround, you can use the Exception Site List feature of your operating system to run the applications blocked by security settings. Adding the URL of the blocked application (applet) to the Exception Site List allows the applet to run with some warnings.

Instead of running the applet, you can download the executable jar file (Java archive) OscillationsE.jar in which several simulations are packaged. When you start it, the list of available simulations appears. Select the simulation Free oscillations of the Torsion Spring Pendulum from this list, and start it together with the presently opened web page, which gives the description of the simulated physical system.

The model of a linear oscillator which is used in the simulation program is a balanced rotor (flywheel) with two equal weights, so that its center of mass lies on the axis of rotation. A spiral spring (with the other end fixed) twists when the wheel turns. The spring creates the restoring torque that tends to return the rotor into the equilibrium position (in this position the needle of the rotor is vertical and points to the zero of the dial). The torque is assumed to be proportional to the angle of deflection (Hooke's law). This angle is measured by the dial points. The whole device is similar to oscillators used in mechanical watches.

After an initial deflection, the rotor, being left to itself, moves towards the equilibrium position with an acceleration provided by the spring. Because of its inertia, the rotor shoots over the equilibrium position and moves further to the opposite side. Now the spring slows it down up to full stop. Then the motion repeats backwards, then again in the same direction, and so on, thus giving rise to oscillations. These oscillations are called free or natural, because they occur without any external driving force.

The model allows you to observe the motion of the pendulum. You can make a pause in the simulation and resume it by clicking on the button "Start/Pause" on the control panel located on the left-hand side of the applet window. You can vary the time scale by moving the slider (named "Delay" – down on the panel to the left side of the pendulum) for convenient observation. The model allows you also to display the graphs of time dependence of the angle and angular velocity (by checking the corresponding check-boxes on the same panel), as well as the graphs of energy transformations and phase diagram. You can resize and drag with the mouse the panels with graphs and the phase trajectory to any convenient place on the screen.

At first acquaintance with the program you can open the list of predefined examples (by using the check-box under the image of the system). These examples illustrate the most typical kinds of motion of the simulated system. Choosing an example from the list, you need not enter the values of parameters required for the illustrated mode – they will be assigned automatically.

The torsion pendulum is characterized by its moment of inertia I about the axis of rotation, and the spring constant D which is the coefficient of proportionality between the restoring torque and the angle of deflection from the equilibrium position. If we use the period of oscillations of the pendulum as a time unit in our mathematical model, then the single parameter remains that completely defines all properties of the system, namely, the dimensionless quality factor Q, that characterises the intensity of viscous friction.

The panel on the right-hand side of the pendulum allows you to vary parameters of the pendulum (absence or presence of viscous friction, and quality factor Q ), and also to change initial conditions of excitation (initial angle of deflection and initial angular velocity). You can change the values either by dragging the sliders, or by typing the desired values from the keyboard (editing the corresponding number fields). In the last case you should press "Enter" key after editing. The model will accept the new values after you press the button "Accept new values".


Principal goals of the lab:

  • To study natural oscillations of a linear mechanical oscillator (torsion pendulum) in the absence of friction.
  • To investigate the energy transformations in the course of natural oscillations.
  • To get acquainted with the phase diagram as a convenient means of graphic representation of oscillations.
  • To study the laws of damping of oscillations at viscous friction.
  • To get acquainted with the interface of simulations programs of a package "Physics of oscillations" by working with the model of a simple physical system.

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