I would use http://en.wikipedia.org/wiki/Lagrangian_mechanics" . It's basically an energy method approach to solving equations of motion for systems with multiple degrees of freedom much more quickly than using Newtonian mechanics. There are examples at the link above.
Actually, to solve this you need more variables and more equations. Instead of phi1 and phi2, use these:
sp1 = sin(phi1)
cp1 = cos(phi1)
sp2 = sin(phi2)
cp2 = cos(phi2)
Adding 2 new equations, you now have these 6 equations:
x0_1 = c1*cp1+c2*cp2
x0_2 = c1*cp1-c2*cp2
v0_1 =...
According to that website, the equatios are:
x1(t) = c1*cos(w1*t+phi1)+c2*cos(w2*t+phi2)
x2(t) = c1*cos(w1*t+phi1)-c2*cos(w2*t+phi2)
Taking the derivative, you get 2 more equations
v1(t) = -c1*w1*sin(w1*t+phi1)-c2*w2*sin(w2*t+phi2)
v2(t) = -c1*w1*sin(w1*t+phi1)+c2*w2*sin(w2*t+phi2)
If your...
It depends on how fast you want it to spin once it's up to speed. The torque will affect how long it takes the blade to get up to speed, but once it's up to speed, the blade doesn't really affect the motor, unless there's significant drag on the blade from air (probably not). There are...
You should probably use a motor with a high gear ratio (motor spins fast relative to the load). This will allow it to have good mechanical advantage so that the 300 lb load will not slow it down.
You didn't give the areas, but by my calculations, it looks like the ratio of the areas of the two cylinders is 7/16. Is that right?
Let's see what you've tried so far and maybe we can spot your error.
Well, both a) and b) look fine. Whichever way you choose, you should realize that you have a nonlinear differential equation. I don't myself know how to analytically solve those (get an equation), though I can get MATLAB to simulate it and plot the results.
What is the initial speed?
Oh...
You could make modifications to increase the car's fuel efficiency. Research about drag on vehicles then make yours more aerodynamic. Measure the car's MPG (miles per gallon) before and after, taking great care to keep everything the same except your mods. Research what things affect MPG...
I assume you're not applying just a constant force to the ends. If that was the case, I'd say just use calibrated scale weights. If you want to vary the force with time, how fast are the vibrations you want to create?
You could get any machine that pushes up and down on the membrane. Measure...
The equation for minimum speed as a function of angle is:
v_min(ang) = (r*g*sin(ang))^0.5
ang = 0 when the body reaches a quarter of the circle
ang = pi/2 when the body reaches the top of the circle
The equation for actual speed as a function of v_top (speed at the top of circle) and...
I made a small mistake in my previous post. You could actually take a picture in any direction upside-down. You would do this by yawing so that you're pointing in the opposite direction, then pitching the camera so that it's inverted to look at the object.
So 0 degrees and 180 degrees are...
So you only have yaw and pitch, but no roll. Camera tripods rotate this way. You can point the camera in ANY direction, so you're not limited there. However, you cannot point the camera at an object and then roll the camera to take an upside-down picture for example. That's what you lose by...