A particle of mass m moves along the horizontal z-axis under the influence of a force...

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A particle of mass m moves along the horizontal z-axis under the influence of a force F away from the origin O in such a manner that its position at any instant of time t is x = x(t) = ne-kt cos wt where the parameters k, ŋ and w are arbitrary positive constants in the real line R = (-∞, ∞). (i) Determine the velocity v = v(t), acceleration a = a(t) and force F which are required to describe the motion of the particle. (ii) Determine the position x = x(t) and velocity v = v(t) of the particle in terms of the arbitrary constants k, n and w when the acceleration a = a(t) is zero. (iii) Draw the position r(t)-t, velocity v(t)- t and acceleration a(t) - t graphs and discuss the changes in the motion of the particle A particle of mass m moves along the horizontal z-axis under the influence of a force F away from the origin O in such a manner that its position at any instant of time t is x = x(t) = ne-kt cos wt where the parameters k, ŋ and w are arbitrary positive constants in the real line R = (-∞, ∞). (i) Determine the velocity v = v(t), acceleration a = a(t) and force F which are required to describe the motion of the particle. (ii) Determine the position x = x(t) and velocity v = v(t) of the particle in terms of the arbitrary constants k, n and w when the acceleration a = a(t) is zero. (iii) Draw the position r(t)-t, velocity v(t)- t and acceleration a(t) - t graphs and discuss the changes in the motion of the particle