APPLICATIONS OF SHM

Applications of

Simple harmonic motion is a motion that is neither driven nor damped. The motion is periodic, as it repeats itself at standard intervals in a specific manner - described as being sinusoidal, with constant amplitude.

Simple harmonic motion is a motion that is neither driven nor damped. The motion is periodic, as it repeats itself at standard intervals in a specific manner - described as being sinusoidal, with constant amplitude.

It is characterized by its amplitude (which is always positive), its period which is the time for a single oscillation, its frequency which is the number of cycles per unit time, and its phase, which determines the starting point on the sine wave.

It is characterized by its amplitude (which is always positive), its period which is the time for a single oscillation, its frequency which is the number of cycles per unit time, and its phase, which determines the starting point on the sine wave.

The period, and its inverse, the frequency, are constants determined by the overall system, while the amplitude and phase are determined by the initial conditions (position and velocity) of that system.

The period, and its inverse, the frequency, are constants determined by the overall system, while the amplitude and phase are determined by the initial conditions (position and velocity) of that system.

 

Variation of acceleration with time Displacement is given by: Velocity is given by differentiating the above equation once: Angular Frequency: Differentiating once more gives us the acceleration: On Simplifying:

 

Mass on a pendulum The above formula is used to express the time period of an ideal pendulum system: L is the length of the pendulum and g is the acceleration due to gravity. This shows that the period of oscillation is independent of both the amplitude and pendulum mass.

Mass on a spring

 

A mass M attached to a spring of spring constant k exhibits simple harmonic motion in space with: Even the formula on the left can be used to calculate the Time period and hence shows that the period of oscillation is independent of both the amplitude and gravity. The total energy is constant which is given by:

Given mass M attached to a spring pendulum with amplitude A with acceleration a : k is the spring constant M is the mass a is the acceleration A is the amplitude OR λ is the wavelength f is the frequency T s or T p is the period of the spring or pendulum g is the acceleration due to gravity is the length of the pendulum E tot is the total energy

Definitions: Amplitude ( A ): The maximum distance that an object moves from its equilibrium position. Period ( T ): The time that it takes for an oscillator to execute one complete cycle of its motion. Frequency ( f ): The number of cycles (or oscillations) the object completes per unit time. Simple Harmonic Oscillator : Any object that oscillates about a stable equilibrium position and experiences a restoring force approximately described by Hooke's law.

Amplitude ( A ): The maximum distance that an object moves from its equilibrium position.

Period ( T ): The time that it takes for an oscillator to execute one complete cycle of its motion.

Frequency ( f ): The number of cycles (or oscillations) the object completes per unit time.

Simple Harmonic Oscillator : Any object that oscillates about a stable equilibrium position and experiences a restoring force approximately described by Hooke's law.

 

Some useful and everyday examples are: a mass attached to a spring, a molecule inside a solid, a car stuck in a ditch being “rocked out”, a pendulum, an electron inside an atom .

 

simple harmonic motion is an effect taking place throughout nature which has many practical applications for human beings.

We must learn how to derive energy from simple harmonic motion as it can be used as a potential energy source especially when the world is surging toward an energy crisis.

We must learn how to derive energy from simple harmonic motion as it can be used as a potential energy source especially when the world is surging toward an energy crisis.

Simple harmonic motion spares no one - ranging from the electron inside an atom to the earth rotating around the sun.

2008-09