SHM of Mass on a Vertical Spring
A mass is attached to a vertical spring and set into motion. The initial position, initial velocity, spring constant, and mass can be varied. Displayed is the position, velocity, and acceleration as function of time. Also calculated are the resulting values of angular frequency, phase angle, amplitude, and maximum velocity. The effects of gravity can observed by turning gravity on and off.

Phase Angle in SHM
The complex relationship between an oscillating object's initial phase angle and the angle of rotation of SHM is displayed along with a mass on a spring undergoing SHM.

Forced Simple and Damped Harmonic Motion
A object on the end of a spring undergoes simple harmonic motion on horizontal surface when there is no friction present. The equations of motion for it position and velocity are displayed, and and can be compared. The system can also be driven by a constant applied force. Without friction the system will still undergo SHM around a new equilibrium poisition. Damped harmonic motion can be observed if friction is turned on. Small values of friction (.10) produced expotential decaying SHM, where as large values of friction produced a critically damped oscillation.

Hook's Law
An object is connected to a spring whose spring constant k can be change along with the object's initial position. Displayed is the spring's force on the object as well a graphical display of the object's position and velocity as function of time. Hook's Law QT Movie(404K)

Energy of Oscillating Bob
A bob oscillates vertically on the end of a spring. The various forms of energy are displayed: the bob's gravitational potential energy, the spring's potential energy, the bob's kinetic energy, and the total mechanical energy of the system of the bob and spring.
Energy of Oscllating Bob QT Movie (300K) & Zero Energy Oscillating Bob QT Movie (300K)

Bar Physical Pendulum
A 2.00 meter bar is pivoted about some point on the bar. The location of the pivot point and the initial angle of the bar from vertical can be varied by clicking and dragging. Displayed is the graph of the angle of oscillation as function of time. Also show are the resulting values of small angle period, momentum of inertia about the pivot point, and the distance of the pivot point from the center of mass of the bar.

Block on a Spring
A block is connected to a horizontal spring and rests on a frictionless surface. In this simulation the amplitude, angular frequency, phase angle, and the mass can be varied. Displayed are the position, velocity, and acceleration of the block as a function of time as well as the resulting values of the period, spring constant, and mechanical energy. Block on a Spring Problem