Reference no: EM132587985
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.
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