A simple approximate formula is derived for the dependence of the period of a simple pendulum on the amplitude. The approximate is more accurate than other simple formulas. Good agreement with experimental data is verified.

We describe a 8085 microprocessor interface developed to make reliable time period measurements. The time period of each oscillation of a simple pendulum was measured using this interface. The variation of the time period with increasing oscillation was studied for the simple harmonic motion (SHM) and for large angle initial displacements (non-SHM). The results underlines the importance of the precautions which the students are asked to take while performing the pendulum experiment.

Since the times of Galileo, it is well-known that a simple pendulum oscillates harmonically for any sufficiently small angular amplitude. Beyond this regime and in absence of dissipative forces, the pendulum period increases with amplitude and then it becomes a nonlinear system. Here in this work, we make use of Fourier series to investigate the transition from linear to nonlinear oscillations, which is done by comparing the Fourier coefficient of the fundamental mode (i.e., that for the small-angle regime) to those corresponding to higher frequencies, for angular amplitudes up to 90 •. Contrarily to some previous works, our results reveal that the pendulum oscillations are not highly anharmonic for all angular amplitudes. This kind of analysis for the pendulum motion is of great pedagogical interest for both theoretical and experimental classes on this theme.

The manuscript details various simple LCR circuits to explain the experimentally observed Surface Plasmon Resonance behavior of spherical metal nano-particles. The results of the circuit’s performance simulated using standard software...

The evaluation of variation in oscillation time period of a simple pendulum as its mass varies proves a rich source of discussion in a physics class-room, overcoming erroneous notions carried forward by students as to what constitutes a pendulum's length due to picking up only the results of approximations and ignoring the rigorous definition. The discussion also presents a exercise for evaluating center of mass of geometrical shapes and system of bodies. In all, the pedagogical value of the problem is worth both theoretical and experimental efforts. This article discusses the theoretical considerations. *