Restoring force

Examples of Restoring force in the following topics:

• Period of a Mass on a Spring

  • The deformation of the ruler creates a force in the opposite direction, known as a restoring force.
  • Once released, the restoring force causes the ruler to move back toward its stable equilibrium position, where the net force on it is zero.
  • The simplest oscillations occur when the restoring force is directly proportional to displacement.
  • The force constant k is related to the rigidity (or stiffness) of a system—the larger the force constant, the greater the restoring force, and the stiffer the system.
  • (c) The restoring force is in the opposite direction.

• The Simple Pendulum

  • This leaves a net restoring force drawing the pendulum back toward the equilibrium position at θ = 0.
  • Now, if we can show that the restoring force is directly proportional to the displacement, then we have a simple harmonic oscillator.
  • Thus, for angles less than about 15º, the restoring force F is
  • For small angles, then, the expression for the restoring force is:
  • Also shown are the forces on the bob, which result in a net force of −mgsinθ toward the equilibrium position—that is, a restoring force.

• Work

  • Forces may do work on a system.
  • This scalar product of force and velocity is classified as instantaneous power delivered by the force.
  • If the force is always directed along this line, and the magnitude of the force is $F$, then this integral simplifies to:
  • The spring applies a restoring force ($-k \cdot x$) on the object located at $x$.
  • Work done by the restoring force leads to increase in the kinetic energy of the object.

• Simple Harmonic Motion

  • Simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement.
  • Simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement (i.e., it follows Hooke's Law) .
  • Simple harmonic motion is typified by the motion of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's Law.
  • The net force on the object can be described by Hooke's law, and so the object undergoes simple harmonic motion.
  • Relate the restoring force and the displacement during the simple harmonic motion

• Hooke's Law

  • F is the restoring force exerted by the spring on that end (in SI units: N or kg·m/s2); and
  • As with any other set of forces, the forces of many springs can be combined into one resultant force.
  • There is a negative sign on the right hand side of the equation because the restoring force always acts in the opposite direction of the displacement (for example, when a spring is stretched to the left, it pulls back to the right).
  • The dotted line shows what the actual (experimental) plot of force might look like.
  • The extension of the spring is linearly proportional to the force.

• What is Potential Energy?

  • Potential energy is often associated with restoring forces such as a spring or the force of gravity.
  • The action of stretching the spring or lifting the mass of an object is performed by an external force that works against the force field of the potential.
  • This work is stored in the force field as potential energy.
  • If the work for an applied force is independent of the path, then the work done by the force is evaluated at the start and end of the trajectory of the point of application.
  • For example, the work of an elastic force is called elastic potential energy ; work done by the gravitational force is called gravitational potential energy; and work done by the Coulomb force is called electric potential energy.

• Work Done by a Variable Force

  • Integration is used to calculate the work done by a variable force.
  • A force is said to do work when it acts on a body so that there is a displacement of the point of application in the direction of the force.
  • Thus, a force does work when it results in movement.
  • The work done by a constant force of magnitude F on a point that moves a displacement $\Delta x$ in the direction of the force is simply the product
  • According to the Hooke's law the restoring force (or spring force) of a perfectly elastic spring is proportional to its extension (or compression), but opposite to the direction of extension (or compression).

• The Meiji Restoration

• Restoration of the Stuarts

  • Lambert was appointed major-general of all the forces in England and Scotland, Fleetwood being general. 
  • The Committee of Safety sent Lambert with a large force to meet George Monck, who was in command of the English forces in Scotland, and either negotiate with him or force him to come to terms.
  • The Presbyterian members, excluded in Pride's Purge of 1648, were recalled, and on December 24 the army restored the Long Parliament.
  • King Charles II, the first monarch to rule after the English Restoration.
  • Evaluate why the Stuarts were brought back and restored to the English throne

• The Last Byzantine Dynasty

  • Michael VIII recaptured Constantinople and restored the Byzantine Empire, giving rise to the last dynasty of the Empire and a brief time of cultural flourishing.
  • At the Battle of Meander Valley, a Turkic force was repelled and an earlier assault on Nicaea led to the death of the Seljuk Sultan.
  • In 1261 CE, Michael's forces succeeded in capturing Constantinople while the Latin knights were off fighting elsewhere.
  • Still, Michael VIII returned to the city and was proclaimed emperor there, marking the restoration of the Byzantine Empire.
  • As the Palaiologan emperors attempted to restore the glory of Constantinople, they sponsored art and encouraged philosophy.