Question

Calculate the normal modes of a one-dimensional chain of atoms of mass M separated by a distance a/2, where the force constants between nearest neighbors alternate between αand 10α. Sketch the dispersion relation ω(q) . Start by evaluating ω(q) at q = 0 and q = 2π/a.

Answer #1

Two waves traveling in opposite directions on a stretched rope
interfere to give the standing wave described by the following wave
function:
y(x,t) = 4 sin(2πx) cos(120πt),
where, y is in centimetres, x is in meters, and t is in seconds.
The rope is two meters long, L = 2 m, and is fixed at both
ends.
In terms of the oscillation period, T, at which of the following
times would all elements on the string have a zero vertical...

Finding the Spring Constant
We can describe an oscillating mass in terms of its position,
velocity, and acceleration as a function of time. We can also
describe the system from an energy perspective. In this experiment,
you will measure the position and velocity as a function of time
for an oscillating mass and spring system, and from those data,
plot the kinetic and potential energies of the system.
Energy is present in three forms for the mass and spring system....

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