In describing beam vibrations using Euler-Bernoulli beam theory, we derived the equation of motion \(\left(\partial^{4} Y / \partial x^{4}\right)-\lambda^{4} Y=0\).

(a) In the equation of motion, what does \(x\) represent physically?
(b) In the equation of motion, what does \(Y\) represent physically?
(c) Write the equation for \(\lambda\) (it replaces several other variables) and describe what each variable represents (include the SI units).