A particle A; of mass 1 kg: moves along a frictionless horizontal track. The par

Question

A particle A; of mass 1 kg: moves along a frictionless horizontal track. The particle is attached to a fixed point O by a model damper, and to another point B by a model spring as shown in the diagram. The two points O and B are a distance 2 meters apart on the track. The damping constant is 7.34 Ns m-1. The spring has stiffness 17.36 Nm-1 and natural length 1.004 meter. The displacement of the particle, x is measured from O. Calculate the equilibrium position of the particle, measured from O, giving your answer to 3 decimal places.

Explanation / Answer

at equilibrium x will be constant,
=> x' = x'' = 0

force equation :   F = mx'' = 0

=> F(spring) - F(damper) = 0

=> F(spring) - B*x' = 0

=> F(spring) - 0 = 0

=> F(spring)

=> k*l = 0

=> l = 0

=> (2-x) - lo = 0

=> x = 2 - lo

=> x = 2 - 1.004

=> x = 0.996 m

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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