200-kg mass is supported by a rope that passes around three small pulleys of neg

Question

200-kg mass is supported by a rope that passes around three small pulleys of negligible mass and is attached to a spring with a modulus of
k2=2kN/m A second spring having a modulus of
k1=3kN/m is also attached to the mass. if the mass is pulled down slightly from the equilibrium position and released from rest, determine
1. the differential equation of the ensuing motion
2. the natural circular frequency
?n of the ensuing motion
3. the natural period
?n of the ensuing motion


the image http://postimage.org/image/qnyo3cc57/

Explanation / Answer

1) mg-k1x+2(k2*2x)=200x

k=k1+k2 wn^2=k/m

fn=wn*(1/2pi)

tau=1/fn

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