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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

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

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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 orbit r=r₂0² Determine (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 energy V(x) given by V(x) = Vo(-x²/2+x²/3) Find the fixed points and their stability? Find the maximum energy for the particle to execute a bound motion? Find the period of small bound oscillations? Sketch the phase space portrait showing the possible types of motion. Point out elliptic and hyperbolic points and the separatrix? (20 points) Q5:Show that the following Lagrangian L=exp/bt/m] (mx-kx)/2 Represents a damped harmonic oscillator? Find the general solution for the damped harmonic oscillator? Discuss the physical interpretation of all the cases and their solutions? (20 points) f(r) = -=--=-= (or " _ ~²²) N
Transcribed Image Text:A particle in a central field moves in the orbit r=r₂0² Determine (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 energy V(x) given by V(x) = Vo(-x²/2+x²/3) Find the fixed points and their stability? Find the maximum energy for the particle to execute a bound motion? Find the period of small bound oscillations? Sketch the phase space portrait showing the possible types of motion. Point out elliptic and hyperbolic points and the separatrix? (20 points) Q5:Show that the following Lagrangian L=exp/bt/m] (mx-kx)/2 Represents a damped harmonic oscillator? Find the general solution for the damped harmonic oscillator? Discuss the physical interpretation of all the cases and their solutions? (20 points) f(r) = -=--=-= (or " _ ~²²) N
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