simple harmonic motion pendulum examples

Let's begin by defining what simple harmonic motion is!įirstly, periodic motion is the type of motion that repeats itself over and over. It's important to note that the SHM is an idealized concept, in many real-world situations the motion may deviate from the SHM due to factors like damping (friction) and external forces. Simple harmonic motion can be seen in many physical systems, such as a mass attached to a spring, a pendulum, and oscillations of an electric circuit.Īny physical system that creates a linear restoring force will exhibit the characteristics of SHM. The energy of the object oscillating in simple harmonic motion is a combination of potential energy (elastic energy stored in the spring) and kinetic energy. The velocity and acceleration of the object also have a sinusoidal form, and the maximum velocity and acceleration occur at the equilibrium position. The frequency (f) is the reciprocal of the period (f = 1/T) Both of these examples will be examined in depth in Applications of Simple Harmonic Motion. The angular frequency (w) and the period (T) of the motion are related by the equation w = 2π/T. Though the spring is the most common example of simple harmonic motion, a pendulum can be approximated by simple harmonic motion, and the torsional oscillator obeys simple harmonic motion. The displacement of the object from the equilibrium position is given by x(t) = A*cos(wt + φ) where A is the amplitude, w is the angular frequency, and φ is the phase angle The variable kappa ( ) is known as the torsion constant of the wire or string. The restoring torque can be modeled as being proportional to the angle. The rigid body oscillates between ( + ) and ( ). The proportionality constant is called the spring constant (k) Figure 15.5.3: A torsional pendulum consists of a rigid body suspended by a string or wire.

The restoring force is always directed towards the equilibrium position and is proportional to the displacement. Here are some key points about simple harmonic motion: The motion of the object is described by a sine or cosine function and is characterized by a restoring force that is proportional to the displacement of the object from the equilibrium position. Simple harmonic motion (SHM) is a type of periodic motion where an object oscillates about a fixed point (equilibrium position) with a constant amplitude and frequency. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. We recommend using aĪuthors: Paul Peter Urone, Roger Hinrichs Use the information below to generate a citation. Then you must include on every digital page view the following attribution:

If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses the The linear displacement from equilibrium is s s size 12 is Figure 16.14 A simple pendulum has a small-diameter bob and a string that has a very small mass but is strong enough not to stretch appreciably.

Simple harmonic motion pendulum examples