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It would help if you could post this using LaTeX (see the LaTeX Guide link at the lower left of the Edit window. Thanks.LCSphysicist said:What you think about this system:?
F*cosw - k(x1+x2) - k(x1-x2) = mx1''
-k(x1+x2) - k(x1-x2) = mx2''
Some sign errors.LCSphysicist said:What you think about this system:?
F*cosw - k(x1+x2) - k(x1-x2) = mx1''
-k(x1+x2) - k(x1-x2) = mx2''
The x1 and x2 can be taken as angles, or arc lengths, whatever.berkeman said:you will need to include the variables θ1 and θ2
Consider the case x1=-x2, so both move the same direction around the hoop. What net forces will spring exert on them? What do your equations give?LCSphysicist said:Maybe the problem is adopt one clockwise and another counterclockwise?
This came to my mind when i attack the problem, but i went on just to see if i could try by this another way as well as adopt just clockwise [or counterclokwise]. But what i can't refut is why would it be wrong, that is:
## F*cos(wt) - [k(x1+x2)] - k(x1-x2) = m \frac{d^2 x1}{dt^2} ##
## [-k(x1+x2)] - k(x1-x2) = m \frac{d^2 x2}{dt^2} ##
the bracket being to the left spring:
If x2 = 0 and x1 > 0, will be a force on m1 in its negative direction, as to x2. Works as well to x1<0
Without bracket to the right spring:
If x2 = 0 and x1 > 0, will be a force on m1 in its negative direction, as to x2. Also works to x1<0
About the Latex, i will try ;)
A driven mass on a circle refers to a system in which a mass is attached to a circular path and is subjected to an external force or torque that drives its motion along the circular path.
The motion of a driven mass on a circle is affected by the magnitude and direction of the external force or torque, the mass of the object, and the radius of the circular path.
The equation for the acceleration of a driven mass on a circle is given by a = (F/m) * r, where a is the acceleration, F is the external force, m is the mass, and r is the radius of the circular path.
The speed of a driven mass on a circle changes with time according to the equation v = ωr, where v is the speed, ω is the angular velocity, and r is the radius of the circular path. As time increases, the speed of the mass increases proportionally to the angular velocity.
Centripetal force is the force that acts towards the center of the circular path and keeps the mass moving along the circular path. It is necessary for maintaining the circular motion of the mass and is equal in magnitude to the centripetal acceleration (ac = v²/r).