A method is proposed to simplify analytical computations of the transfer function for electrical circuit filters, which are made from repetitive identical stages. A method based on the construction of Pascal's triangle is introduced and then a general solution from two initial conditions is provided for the repetitive identical stage. The present…

We examine a generalization of the one-dimensional Ising model involving interactions among neighbourhoods of "k" adjacent spins. The model is solved by exploiting a connection to an interesting computational problem that we call ""k"-SAT on a ring", and is shown to be equivalent to the nearest-neighbour Ising model in the absence of an external…

In this research we asked the fourth year students (N = 50) of a technical faculty of the University of Split (Republic of Croatia) to solve a partially specified physics problem related to gravitational force. The task for the students was to decide whether the situation described in the problem is feasible or not. Nevertheless, the formulation…

Dimensional analysis, superposition principle, and continuity of electric potential are used to study the electric potential of a uniformly charged square sheet on its plane. It is shown that knowing the electric potential on the diagonal and inside the square sheet is equivalent to knowing it everywhere on the plane of the square sheet. The…

We propose a simple and straightforward method based on Wronskians for the calculation of bound-state energies and wavefunctions of one-dimensional quantum-mechanical problems. We explicitly discuss the asymptotic behaviour of the wavefunction and show that the allowed energies make the divergent part vanish. As illustrative examples we consider…

This paper outlines the solution that the Team of Austria found to problem number 7, "skateboarder", presented in the finals of the 22nd International Young Physicists' Tournament (IYPT) in Tianjin, China. We investigated how a skateboarder can accelerate from rest on a horizontal surface without touching an external support. The focus was laid on…

We examine the Stark effect (the second-order shifts in the energy spectrum due to an external constant force) for two one-dimensional model quantum mechanical systems described by linear potentials, the so-called quantum bouncer (defined by V(z) = Fz for z greater than 0 and V(z) = [infinity] for z less than 0) and the symmetric linear potential…

A pendulum with periodically varying length is an interesting physical system. It has been studied by some researchers using traditional perturbation methods (for example, the averaging method). But due to the limitation of the conventional perturbation methods, the solutions are not valid for long-term prediction of the pendulum. In this paper,…

This paper enlarges the reservoir of solved tutor problems in non-holonomic mechanics at the undergraduate level of physics education. Unlike other, rather artificial, solved problems typically used, the streetboard-rider locomotion problem presented here represents an appealing contemporary real-world problem with interesting applications in a…

A number of cars drive along a narrow road that does not allow overtaking. Each driver has a certain maximum speed at which he or she will drive if alone on the road. As a result of slower cars ahead, many cars are forced to drive at speeds lower than their maximum ones. The average velocity in the queue offers a non-trivial example of a mean…

This paper presents an original undergraduate student project in theoretical mechanics: a demonstration of theory and experiment agreement inspired by a recently theoretically treated mechanical problem of coupled rolling motion of two cylinders. The problem of a mechanical system subjected to non-holonomic constraints is theoretically and…

The problem of motorbike feathering has been analysed by writing the angular momentum theorem for non-inertial reference systems. The acceleration, for which the ideal line joining the median points of the axles of the two wheels makes an angle [theta] with the horizontal, has been calculated neglecting air friction and considering that the…

In this paper, we take a look at two electrostatics problems concerning hemispheres. The first problem concerns the direction of the electric field on the flat cap of a uniformly charged hemisphere. We show that the symmetry and principle of superposition coupled with Gauss's law gives a delightfully simple solution and then go on to examine how…