Introduction

## 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. You can also choose for the spring to behave like a spring only when stretched, and have no effect when compressed (i.e. it is more like a string).

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

Activities

## Activities

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.
5. Also try activating the "string-like" mode such that the elastic force only occurs in the stretched state and not in the compressed state.

### Translations

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### Software Requirements

SoftwareRequirements

 Android iOS Windows MacOS with best with Chrome Chrome Chrome Chrome support full-screen? Yes. Chrome/Opera No. Firefox/ Samsung 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

### Credits

Wolfgang Christian; Francisco Esquembre; Zhiming Darren TAN

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Research

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