URGENT. please solve now
Q.3. Consider a one dimensional motion of a particle of mass m under a conservative force field. The corresponding potential energy is given as, U(x) =-x+62x", where, ci and c, are greater than zero with appropriate dimensions. (a) Obtain the equation of motion of the particle in terms of the variable x. (b) Assume that the particle starts from x = 0) with a velocity epi. At what value of x=0, it will attain the same velocity eyi again? (c) Determine the stable/unstable equilibrium point(s) of the potential and hence, obtain the frequency of small oscillations about the stable equilibrium point(s). (d) Now assume that the particle starts from x = 0 and moves under the above potential in the presence of friction due to the surface (# being the coefficient of friction). What should be particle's velocity v at x = 0, so that it barely reaches the stable equilibrium point? The answers should be written in terms of cs.c. m, u and g, wherever applicable. (4+2+3+6+5)
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