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Projectile Motion with System of Masses and Spring

This is the simulation of the motion of two masses m and m1 situated at the ends of a spring of length L0 and negligible mass. The motion is restricted to two spatial dimensions, with the y-axis representing the vertical (if gravity is switched on).

We use Hooke's law for the spring force, and include a damping term that is proportional to the difference of the velocities of the masses on both ends of the spring.

Applying Newton's Second Law yields a second-order ordinary differential equation, which we solve numerically in the simulation and visualise the results.



  1. Drag the red mass to impart an initial velocity, and see how the system evolves.
  2. Observe what happens when you do the same, but with gravity switched on.
  3. Try changing the relative mass of the blue ball, and notice how the centre of gravity shifts.
  4. Try varying the spring constant and/or the damping coefficient while the simulation runs.


Software Requirements


Android iOS Windows MacOS
with best with Chrome Chrome Chrome Chrome
support fullscreen? Yes. Chrome/Opera No. Firefox/ Sumsung Internet Not yet Yes Yes
cannot work on some mobile browser that don't understand JavaScript such as..... cannot work on Internet Explorer 9 and below



Wolfgang Christian; Francisco Esquembre; Zhiming Darren TAN

end faq




Other resources

  1. Illustration 3.4: Projectile Motion by W. Christian and M. Belloni 
  2. Trajectory of a ball with air resistance by Farhang Amiri
  3. HTML5 version of Projectile Motion by Walter Fendt
  4. Ejs Intro 2DMotionLab Model by  Anne Cox, Wolfgang Christian, and Mario Belloni 
  5. Projectile motion with equations by Fu-Kwun Hwang
  6. Airdrag by Fu-Kwun Hwang and ahmedelshfie
  7. Simulation of BasketBall Throw by Lew W. S.
  8. by This email address is being protected from spambots. You need JavaScript enabled to view it.
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