I want to modify our swing so that springs in the chains absorb half the high velocity at the bottom of the swing so that the kids get a smoother ride and so that there is 1/2 the air friction losses. I have not yet figured out how to add a controlled motor to give it energy. The energy from the swing is absorbed into the spring as it falls and released when it rises, reducing maximum speed at the bottom, but returning closer to the same initial height. Need to know spring constant for ordering/making and distance it will stretch.
Swing plus kid = 88 pounds, 44 pounds per chain+spring = 20 kg = m
Chain+spring length after spring is stretched to max = L = 3 meters
Max height of swinging = h = 1 meter = 1/3 L
Max velocity without spring = V
g = 10 m/s^2
Shoot for 1/2 energy stored in spring, (0.707*V)^2 = 0.5*V^2.
Total energy from dropping = mgh =m*1/3*L = 1/2*m*V^2 = 2*1/2*k*x^2 (1)
solving a little gives V^2 = 2/3*L (2)
Force at bottom of swinging = m+m*Vo^2/R = m+m*(0.707*V)^2 / L = k*x (3)
Plugging (3) into (1) and (2) into (3):
[k*x]*x = [ m+m*(0.707*V)^2 / L ]*x = [m+m/3] => k*x = 4/3*m
I want spring to oscillate with pendulum:
SQRT( k/m ) = SQRT (g / L) => k=mg/L = 67 N/m => x=4*L/(3g) = 0.4 meters stretch. hmmm I wonder what kind of initial length that requires.
Chains have been tested to 400 pounds each.