Motocross Engineer

You're on the team designing the best motocross bike for Ricky Carmichael, AKA the GOAT, for his grand reappearance on the AMA Championship stage.

Your role is to design the damping controls in the shock absorbers to most effectively handle those hard landings. Upon impact, the motocross bike bounces according to the following equation:

quadratic_differential_eq.png

To optimize shock absorption, or maximally reduce oscillation after impact, which damping scenario should your design strive for?

Deviate From The Ideal...

...Gas Law! All real gases deviate to some extent from the ideal behavior described by the Ideal Gas Law equation pV = mRT . For which of the following conditions are the deviations smallest?

(Physics) Minimum Total Mechanical Energy

Consider the following sketch of potential energy for a particle as a function of position. 
There are no dissipative forces or internal sources of energy. What is the minimum total mechanical energy that the particle can have if you know that it has traveled over the entire region of X shown?

 

Note: Even if you don't know, guess! Then learn from the solution for next time!

(Physics) Block Attached to Spring on Incline

A block of mass m is attached to a relaxed spring on an inclined plane. The 
block is allowed to slide down the incline, and comes to rest. The coefficient of kinetic 
friction of the block on the incline is µk. For which definition of the system is the change 
in total energy (after the block is released) zero? 

Arduino Clock (Electronics)

 

Getting up in the morning is hard. After coming across the Chlonos Arduino Clock, you decide to make your own alarm clock...(that speaks to you while flashing awesome looking optics.)

First you get the parts: a speech synthesizer, a speaker, an LED display, a realtime clock, a temperature sensor, a 9V battery, and some AA batteries. 

What does the temperature sensor voltage (V1) and clock voltage (V4) need to be to ensure optimal performance?