Question

4. 3D isotropic and anisotropic harmonic oscillators A particle of mass m is attached on both sides to a pair of light springs with a spring constant k along each of the Cartesian coordinate axis; x-, y- and z-axis. a) If the springs in all three directions have the same spring constant k; i) write the equation of motion (EOM) for the particle and its general solutions. ii) use relevant octave script to solve and plot the position of the particle as a function of time. iii) describe the state of motion of the particle based on the plots in part ii). b) If the springs in all three directions have different spring constants; i) write the equation of motion (EOM) for the particle and its general solutions. ii) use relevant octave script provided to solve and plot the position of the particle as a function of time. iii) describe the state of motion of the particle based on the plots in part ii).

          4. 3D isotropic and anisotropic harmonic oscillators
A particle of mass m is attached on both sides to a pair of light springs with a spring constant k along each of the Cartesian coordinate axis; x-, y- and z-axis.
a) If the springs in all three directions have the same spring constant k;
i) write the equation of motion (EOM) for the particle and its general solutions.
ii) use relevant octave script to solve and plot the position of the particle as a function of time.
iii) describe the state of motion of the particle based on the plots in part ii).
b) If the springs in all three directions have different spring constants;
i) write the equation of motion (EOM) for the particle and its general solutions.
ii) use relevant octave script provided to solve and plot the position of the particle as a function of time.
iii) describe the state of motion of the particle based on the plots in part ii).

4. 3D isotropic and anisotropic harmonic oscillators
A particle of mass m is attached on both sides to a pair of light springs with a spring constant k along each of the Cartesian coordinate axis; x-, y- and z-axis.
a) If the springs in all three directions have the same spring constant k;
i) write the equation of motion (EOM) for the particle and its general solutions.
ii) use relevant octave script to solve and plot the position of the particle as a function of time.
iii) describe the state of motion of the particle based on the plots in part ii).
b) If the springs in all three directions have different spring constants;
i) write the equation of motion (EOM) for the particle and its general solutions.
ii) use relevant octave script provided to solve and plot the position of the particle as a function of time.
iii) describe the state of motion of the particle based on the plots in part ii).

Added by David M.

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