- Parent Category: 02 Newtonian Mechanics
- Category: 09 Oscillations
- Created: Friday, 16 October 2020 12:02
- Last Updated: Friday, 16 October 2020 12:13
- Published: Friday, 16 October 2020 12:02
- Written by Z. Darren Tan
- Hits: 821
Mass on a Spring: Motion in a Vertical Plane
A mass m is situated at the end of a spring of (unstretched) length L0 and negligible mass. The spring is fixed at the other end and the motion is restricted to two spatial dimensions in a vertical plane, with the y-axis representing the vertical (if gravity is switched on).
We use Hooke's law (with spring constant k) for the spring force, and include a damping term that is proportional to the velocity of the mass. 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.
- Drag the red mass to impart an initial velocity, and see how the system evolves.
- Try changing the initial vertical position of the mass relative to the fixed end of the spring using the slider.
- Observe what happens when gravity is switched off.
- Try varying the spring constant relative to the force of gravity and/or the damping coefficient, using the sliders. You may need to fiddle with the damping coefficient to better approximate energy conservation.
- Also try activating the "string-like" mode such that the elastic force only occurs in the stretched state and not in the compressed state.
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Wolfgang Christian; Francisco Esquembre; Zhiming Darren TAN
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