A shock absorber is a mechanical device which provides resistance to compression

Question

A shock absorber is a mechanical device which provides resistance to compression or extension given by R= cv, where c is a constant and v is the time rate of change of the length of the absorber. An absorber of constant c=3000N * s/m is shown being tested with a 100 kg cylinder suspended from it. They system is released with the cable taut at y=0 and allowed to extend. Determine (a) the steady-state velocty v_s of the lower end of the absorber and (b) the time t and displacement y of the lower end when the cylinder has reached 90 percent of its steady-state speed. Neglect the mass of the piston and attached rod. Please show all work.

Explanation / Answer

governing differential equation is given by

m*a + c*v = m*g

a)

at steady state, a = 0

=> v(steady) = m*g/c = 100*9.8/3000 = 3.267 m/s

b)

m*y" + c*y' = m*g

Complementary function solution:

m*y" + c*y' = 0

let y = et

=> m*2 + c* = 0

=> =0, -c/m

=> = 0, -30

thus, yc = c1 + c2*e-30t

for particular integral solution:

(m*D2 + c*D)y = m*g

=>yp = m*g/(m*D2 + c*D)

thus find particular integral solution from above.

thus y = yc + yp

now v = y'

thus put v = 0.9*3.267 to find time and displacement.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.