Mathematical Methods and Mechanics

Question 3

A particle A, of mass I 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 Figure Q3. The two points O and B arc a distance 2 metres-apart on the track. The damping constant is 6 Ns m-'. The spring has stiffiress 9 Nm-l and natural length I metre. The displacement of the particle, x, is measured from O.

r=6 a k:9m=l h=l Fisure 03

(a) Draw a force diagram for the particle, indieating only the forces that cause the oscillations, and define these forces.

(3 marks)

(b) Derive the equation ofmotion of the particle. (5 marks)

(c) What is the equilibrium position of the particle, measured from O? (3 marks)

(d) The particle is initially projected from its equilibrium position towards the point B. Describe briefly and qualitatively the subsequent motion of the particle.

(2 marks) Ngte : Do not solve the equation of motion.