Newton’s Second Law is the backbone of Physics I. You have learned about accelerations and kinematics. Most textbooks avoid mentioning what is causing those accelerations during the chapters on kinematics. Newton’s First Law let us know that forces cause things to accelerate. Newton’s Second Law tells us how forces and accelerations are related.

In modern mathematical usage, we write Newton’s Second Law in mathematical form as…

\(\color{black}{\Sigma \vec{F} = m \vec{a}}\)

## Goal of the Course

By working through this course, you will begin to understand Newton’s Second Law. Then you can apply it in situations where multiple forces are applied to a single object. We will start by looking at one dimensional examples, then progress to two dimensions.

I was watching your damped harmonics video on youtube. I have a problem where I want to create a drive file for matlab. However it is a amplified problem. My electrical engineering teacher doesn’t know how the physical system works and I am at a Junior college. I am trying to make a sine or cosine function that would emulate a “4 post” rig suspension input. SO something on the order of f(x)=Ae^(-2x)cos(wprime(x)+phi). Also an explanation of what the values are would be great. ie ” where -2 = the damping coefficient etc. So I can source the correct inputs. I JUST finished math 111 and I am starting 112. The function would look the opposite. So starting with low amplitude and going to high on the range of 0(or 1) to 20 hz on the x axis.

By one of the FSAE judges that I know gave me a hint of:

“A first order low pass filter will work if you’re trying to maintain equal peak velocity as frequency changes.”

“Halve the amplitude for every doubling of frequency”

Adding a driver makes things a bit more complicated. Essentially, though, you are adding a driven term to the final solution. That term should look like Bcos(omega2*t-phi2). Here, B is the amplitude of the driver, omega2 is the angular frequency of the driver (close to the oscillator’s) and phi2 is a phase angle for the driver.

See http://hyperphysics.phy-astr.gsu.edu/hbase/oscdr.html

You can also see or http://farside.ph.utexas.edu/teaching/315/Waves/node13.html.