Some specific gravitational potential energy and its force
Question: Newtonian theory of gravity can be modified at short range. Such potential energy between two objects is given as […]
Magnetic fields created by a parallel circuit with resistors
Question: The wire splits into two ways, which are bent circularly with radius of \(a\). The upper half wire has […]
Solving for the eigenvalue and eigenvector of a matrix
Question: (1) Find the eigenvalues and eigenvectors of a matrix, \[ A=\left(\begin{array}{c}-5 & 6\\-4 & 5\end{array}\right) \] (2) If \(C\) […]
Wave equation of the horizontal spring motion
Question: An object attached to a spring moves on a horizontal frictionless surface. This is a harmonic motion with amplitude […]
RC circuit with a DC power supply when the resistances connected in parallel
Question: Consider an RC circuit with a DC voltage supply as shown in the figure. There are four identical resistors […]
Speed of sound in water: The wave speed in different media
Question: The bulk modulus of water is 2.04\(\times\)10\(^9\) Pa. The frequency of a water wave is found to be 262 […]
Damped oscillation of a spring motion: Linear differential equation
Question: A 0.400-kg bob is attached to a spring of its force constant \(k=200\) N/m and this motion is subject […]
Hydrogen molecules in thermal and quantum system
Question: There are hydrogen molecules contained in a closed system by contacting a heat bath at \(T=300\) K. Find the […]
Conditions for the regular function: Complex variables
Question: Consider a complex function, \(f(z)=u(x,y)+iv(x,y)\). When \(u(x,y)=\frac{x}{x^2+y^2-2y+1}\), find the \(f(z)\) which can be a regular function. Answer: According to […]
Proving the charges of proton, neutron, and pi meson
Question: Consider a proton, a neutron, and \(\pi\) mesons. These are also called hadrons which are constructed with quarks. Particularly, […]