6. A particle of mass m moves on the r-axis under a force F(x)=3(x-a)(x - 1) where a is a constant. (a) Use Newton's sec

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6 A Particle Of Mass M Moves On The R Axis Under A Force F X 3 X A X 1 Where A Is A Constant A Use Newton S Sec 1 (40.21 KiB) Viewed 501 times

6. A particle of mass m moves on the r-axis under a force F(x)=3(x-a)(x - 1) where a is a constant. (a) Use Newton's second law, Fm, to derive the energy equation mi²+V(x) = Eo. where Eo is a constant and where the potential V(r) is a function of a depending on the parameter a which you are asked to determine. [4 marks] (b) Determine a so that the potential V(r) = 3r-r³ and plot V(x). [3 marks] (c) We shall assume that V(z) = 3x - ³ from now on. Find the equilibrium points of the system and determine their stability. [4 marks] (d) Assuming that the particle is fired from the origin with velocity = 1, determine mmar, the maximum value of m, below which the particle's motion must be oscillatory. [4 marks]