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# Mass attached to a vertical spring

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A mass m is attached to a vertical spring (with a spring constant k). Any source of friction is neglected. The equation of motion of the mass is given by

m(d^2x/dt^2) = mg - kx

where g is the constant of gravitation and x refers to the vertical position of the mass. Solve this equation to find the function x(t), assuming that at t = 0 we have x = x_0 and dx/dt = 0. Draw x(t), x(t), and x(t).

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The solution is attached below in two files. The files are identical in content, only differ in format. The first is in MS Word format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.

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The equation is:
(1.1)

We shift the coordinates to a new coordinate:
...

#### Solution Summary

The expert examines the mass attached to a vertical spring.

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