may you please solve Q3 for me. Note, this is not an assignment or an exam. those are past paper questions and I am trying to prepare for finals, so please guide me through A particle in a central field moves in the orbitr=r₂0²Determine (a) the force function and the potential energy function; and((b) how the angle 0 varies with time. (20 points)a)b)c)d)Q4: A particle of mass m moves along the x axis with potential energyV(x) given byV(x) = Vo(-x²/2+x²/3)Find the fixed points and their stability?Find the maximum energy for the particle to execute a boundmotion?Find the period of small bound oscillations?Sketch the phase space portrait showing the possible types ofmotion. Point out elliptic and hyperbolic points and the separatrix? (20points)Q5:Show that the following LagrangianL=exp/bt/m] (mx-kx)/2Represents a damped harmonic oscillator?Find the general solution for the damped harmonic oscillator?Discuss the physical interpretation of all the cases and their solutions? (20points)f(r) = -=--=-= (or " _ ~²²)N

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HW Help: Just part C, Thank you!
Solve it correctly please.
Problem #2
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please include the full solution so i can make sure mine is correct.
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A particle in a central field moves in the orbit r=r,0² 925 Determine (a) the force function and the potential energy function; and (b) how the angle 0 varies with time. (20 points) 04: A particle of mass m moves along the x axis with