Question bank: Simple Harmonic Motion: Definition

Simple Harmonic Motion (SHM) is an oscillatory motion that occurs when a body, subject to a restoring force, moves periodically around an equilibrium point. The mathematical expression that describes this motion is given by the formula y = A.sin(ωt + φ). Which of these parameters represents the initial position of the body at time t = 0?

A pianist plays a key on his piano whose string is in vibratory motion. This movement is closely related to Simple Harmonic Motion (SHM). The frequency of the musical note produced by the string is 440 Hz and the oscillating mass at the end of the string is 2g. Consider that the oscillation's amplitude is 5mm.

A young girl observes the swing of a simple pendulum in the leisure square of her school. She notices that the pendulum's movement is repetitive and follows similar patterns. Based on this observation, she wants to understand if the pendulum's movement is an example of Simple Harmonic Motion (SHM). (a) Define Simple Harmonic Motion, describing its main characteristics. (b) Considering the definition of SHM, explain if the pendulum's movement fits into this category or not. (c) If the answer is affirmative, explain what condition must be met for a simple pendulum to perform SHM. If the answer is negative, indicate the necessary conditions for a movement to be considered simple harmonic.

The equation of harmonic oscillation is used to describe the behavior of Simple Harmonic Motion (SHM). This equation is given by F=-kx, where F is the force, k is the spring constant, and x is the displacement of the particle from its equilibrium position. Which of these characteristics is NOT related to SHM?

A simple pendulum is a point mass attached to a massless rod that oscillates around an equilibrium point under the action of gravitational force. At the lowest point of its trajectory, the pendulum has maximum acceleration. Consider a simple pendulum of length 1 meter that is displaced from its equilibrium position and released. The pendulum undergoes simple harmonic motion (S.H.M) if the angle of displacement from the equilibrium position is small. Determine if the pendulum's motion can be considered S.H.M. and justify your answer by applying the definition of S.H.M. and relating it to the maximum tolerable displacement angle for the approximation of the sine of an angle to the angle itself. Consider g = 9.8 m/s^2 and use the fact that, for small angles, sin(θ) ≈ θ in radians.