Question

Consider N masses connected by springs to each other and the walls on both sides. • To start, choose both the masses and the spring constants as 1. Set up the eigenvalue problem and solve it for $N$ = 2, 3, 4, 5, 10, 15, 20, 30, 50, 70, 100. You'll need some com- puter method, e.g., Mathematica, Python, ..., once you go beyond $N$ = 3. • Sketch the fundamental modes for $N$ = 3, 4, 5. • Plot the spectrum of angular frequencies. • Investigate what happens if every other mass is doubled from its original value, i.e., the masses are now lined up as 1, 2, 1, 2, ....

          Consider N masses connected by springs to each other and the walls on both sides.
• To start, choose both the masses and the spring constants as 1. Set up the eigenvalue
problem and solve it for $N$ = 2, 3, 4, 5, 10, 15, 20, 30, 50, 70, 100. You'll need some com-
puter method, e.g., Mathematica, Python, ..., once you go beyond $N$ = 3.
• Sketch the fundamental modes for $N$ = 3, 4, 5.
• Plot the spectrum of angular frequencies.
• Investigate what happens if every other mass is doubled from its original value, i.e., the
masses are now lined up as 1, 2, 1, 2, ....

Consider N masses connected by springs to each other and the walls on both sides.
• To start, choose both the masses and the spring constants as 1. Set up the eigenvalue
problem and solve it for N = 2, 3, 4, 5, 10, 15, 20, 30, 50, 70, 100. You'll need some com-
puter method, e.g., Mathematica, Python, ..., once you go beyond N = 3.
• Sketch the fundamental modes for N = 3, 4, 5.
• Plot the spectrum of angular frequencies.
• Investigate what happens if every other mass is doubled from its original value, i.e., the
masses are now lined up as 1, 2, 1, 2, ....

Added by Amber N.

Question

Please give Ace some feedback