Find the general solution to the equation of motion

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Question 1 - (i) Calculate the acceleration a ?(t) and give its components that are tangential and normal to the trajectory of the particle.

(ii) If m is the mass of the particle what force F~(t) acts on the particle and what work is performed by this force during the time interval from t0 = 0 to t1 = π/ω?

Question 2 - A particle of mass m moves on the x axis under the action of the force F1(x) = -kx, where k is a positive constant.

a) (i) Employ Newton's 2nd law to write down a differential equation of motion.

(ii) Find the general solution to the equation of motion.

(iii) Determine the potential V (x) of the force F1 assuming that V (0) = 0.

(iv) Employ conservation of energy to find a relation between position x and velocity x? of the particle for a prescribed value E0 of the total energy.

b) Assume that in addition to the force F1(x) there is also a strong damping force

F2 (x ?) = -vx, v = constant, v > √km.

Reference no: EM132587985

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