As much as we like to talk about vibes, actual vibrations underlie pretty much everything about the universe. From the patterns of galaxies created by the Big Bang to the existence of subatomic particles, here's how the universe runs on...

Earthquakes have always been a terrifying phenomenon, and they've become more deadly as our cities have grown - with collapsing buildings posing one of the largest risks. But why do buildings collapse in an earthquake? And how can it be...

As small as Jupiter's moons are in comparison to the giant planet, they may actually have an important role to play in keeping each other warm, heating the moons enough to have liquid oceans!

By arranging definitions it's possible to find the value of our damping ratio and natural frequency in terms of our spring constant and damping coefficient.

This is an alternate proof for finding the natural frequencies and natural modes for a 2 DOF system. This method can always be used, but it's easier to involve matrices for larger degrees of freedom.



The equation of motion...

Here I describe the main formulas used for harmonic excitation.


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TIME
STAMPS
0:00 - Introdu
ction
0:27 - Experiment Resul
ts
0:51 - Forced Vi
bration SMD...

Two blocks oscillating via springs is a 2 DOF system. The final solution will have the form of a



a modal vector times cos(w1t - phi1) + another modal vector times cos(w

2t -phi2).

The system is hence said to be...

Here I derive part of the equation of motion for a spring mass damper system experiencing a sinusoidaly varying force. This is only the particular solution - Ie, the steady state solution. The total solution is x(t) = x_p + x_h where x_h...

Math and physics can show up when you least expect

This is a summary of all the videos we've made so far. Notice that our total response = our steady state (particular solution) + our transient (homogeneous solution).



In most Engineering applications we will only focus on the...

This is the frequency, amplitude and period for simple harmonic motion (ie, no damping effects)

Here I derive the formula used for logarithmic decrement. This is way to experimentally determine the values of your damping ratio. To do it:

1) Find the maximum amplitudes of your first peak and second
peak
2) Find delta...

Try to sing the impossible note! Singers try to sing into a pipe, and find certain notes are impossible to sing, even for professionals. WHY?! More facts: Most objects have a number of different resonant frequencies. The first resonance...

This video engages students by asking questions and showing phenomena that relate to simple harmonic motion. The program provides examples and demonstrations using “singing” glasses, violin and piano sounding boards, oscillations in...

Resonance is introduced and demonstrated using a “singing rod”, a swing, a goblet, a hollow tube in water, a hollow tube open on both ends, a seashell, a broken speaker, a human body and a key fob, and a shorter “singing rod”....