(25 marks) Question 2 (2.1) A particle of mass m is attached to two identical springs of modulus k and unperturbed lengt

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25 Marks Question 2 2 1 A Particle Of Mass M Is Attached To Two Identical Springs Of Modulus K And Unperturbed Lengt 1 (56.75 KiB) Viewed 35 times

(25 marks) Question 2 (2.1) A particle of mass m is attached to two identical springs of modulus k and unperturbed length L, which are in turn attached to walls: Initially, the particle's velocity is v>0. Find the maximum displacement of the particle. (2.2) A thin rod of mass m and length L is rotating around its end with angular velocity . Calculate the rod's kinetic energy. (2.3) A body of mass m is attached to the ceiling by a spring of unperturbed length I and modulus k. (2.3a) Find the distance Heg between the body's equilibrium position and the ceiling. (2.3b) Assuming that the drag (friction) force is Fuv (μ is the friction coefficient, v is the velocity of the body), derive an equation for the distance x(1) between the body's current and equilibrium positions ( is the time). (2.3c) Assuming that m=2, k = 8, and μ = 8, determine whether the oscillations of the body are underdamped, overdamped, or critically damped. Draw a typical graph of x(1). (2.4) Consider two particles of masses m, and m, separated by a distance I, and an object located on the straight line connecting them. Where should the object be placed so that the gravity forces exerted on it by the particles are in exact balance?