Question

Unforced Simple Harmonic Motion Spreadsheet

Answer 1

The attached spreadsheet is one that I developed that allows the user to analyze and better understand the motion associated with a body undergoing simple harmonic motion.

Using Newton’s second law, Hooke’s law of an ideal spring, and if we assume the resistance of the system produces a force proportional to velocity we obtain the second-order linear differential equation:
\[my''+cy' + ky = 0 \]
Where m is that mass of a oscillating object, c is the the damping constant, and k is the spring constant. The damping constant can be thought of as how strongly the damper (dashpot) resists movement and the spring constant can be thought of as how stiff the spring is.

Using elementary mathematics, we can solve this equation and predict the vibratory motion of a mass-spring-dashpot system. This spreadsheet does just that.

To use the spreadsheet the user must declare the values of c, m and k, as well as the amount of time the graph should extend and the number of points to evaluate the function at. He/she then presses "Calculate" and the program will solve the equation and graph the position with respect to time given the inputted parameters. As an added bonus the program will also graph the "Phase Space", velocity with respect to position.

This program is most beneficial, not in actually solving the differential equations as these are easy to solve, but in allowing the user to play around with the constants so that they can understand what exactly changing c, m and k does to the vibratory motion of the object.

Hope you guys like it. =)

Answer 2

thanks!

Answer 3

THIS IS AWSOME

Answer 4

Thanks @UnkleRhaukus ! If someone ever gives you a shm problem you can refer to this as a model.

Answer 5

oh and i will, my studying physics and i bet ill use this excel document many many times,
thank you so much