Learning Goals: Define wavelength, frequency, period, and amplitude. Describe the relationship between frequency and wavelength. Explain how a wave's. Chapter Goal: To understand systems that The characteristic equation for SHM is a cosine function. period, T. The frequency, f, is the number of cycles per second. . frequency. • The amplitude of oscillations is generally not very high if f. Learning Objectives For the object on the spring, the units of amplitude and displacement are meters; whereas One special thing is that the period T and frequency f of a simple harmonic oscillator are independent of amplitude. . x=X. The minus sign in the first equation for v(t) gives the correct direction for the velocity.

The pendulum is contained inside. One of the earliest known uses of a pendulum was a 1st-century seismometer device of Han Dynasty Chinese scientist Zhang Heng.

Galileo's research Italian scientist Galileo Galilei was the first to study the properties of pendulums, beginning around He first employed freeswinging pendulums in simple timing applications. His physician friend, Santorio Santoriiinvented a device which measured a patient's pulse by the length of a pendulum; the pulsilogium. The pendulum clock The first pendulum clock In the Dutch scientist Christiaan Huygens built the first pendulum clock.

This played a part in Newton's formulation of the law of universal gravitation. From this he deduced that the force of gravity was lower at Cayenne. Huygens' Horologium Oscillatorium In17 years after he invented the pendulum clock, Christiaan Huygens published his theory of the pendulum, Horologium Oscillatorium sive de motu pendulorum. By a complicated method that was an early use of calculushe showed this curve was a cycloidrather than the circular arc of a pendulum, [48] confirming that the pendulum was not isochronous and Galileo's observation of isochronism was accurate only for small swings.

### Amplitude, Period, Phase Shift and Frequency

Temperature compensated pendulums The Foucault pendulum in was the first demonstration of the Earth's rotation that did not involve celestial observations, and it created a "pendulum mania". In this animation the rate of precession is greatly exaggerated. During the 18th and 19th century, the pendulum clock 's role as the most accurate timekeeper motivated much practical research into improving pendulums.

It was found that a major source of error was that the pendulum rod expanded and contracted with changes in ambient temperature, changing the period of swing. Huygens had discovered in that a pendulum has the same period when hung from its center of oscillation as when hung from its pivot, [17] and the distance between the two points was equal to the length of a simple gravity pendulum of the same period. For the next century the reversible pendulum was the standard method of measuring absolute gravitational acceleration.

Foucault pendulum Main article: Decline in use Around low- thermal-expansion materials began to be used for pendulum rods in the highest precision clocks and other instruments, first invara nickel steel alloy, and later fused quartzwhich made temperature compensation trivial. Clock pendulums Longcase clock Grandfather clock pendulum Ornamented pendulum in a French Comtoise clock Mercury pendulum Gridiron pendulum Ellicott pendulum, another temperature compensated type Invar pendulum in low pressure tank in Riefler regulator clockused as the US time standard from to Use for time measurement Pendulum and anchor escapement from a grandfather clock Animation of anchor escapementone of the most widely used escapements in pendulum clock.

For years, from its discovery around until development of the quartz clock in the s, the pendulum was the world's standard for accurate timekeeping. Pendulums require great mechanical stability: Pendulum clock Pendulums in clocks see example at right are usually made of a weight or bob b suspended by a rod of wood or metal a.

In quality clocks the bob is made as heavy as the suspension can support and the movement can drive, since this improves the regulation of the clock see Accuracy below. A common weight for seconds pendulum bobs is 15 pounds 6. This lesson will guide you through the five wave parameters - period, frequency, amplitude, wavelength, and speed - that we use to characterize waves. Wave Parameters So, we've learned a little bit about waves, right? We've learned that waves originate from vibrations, which are oscillating motions over a fixed position.

A vibration can cause a disturbance to travel through a medium, transporting energy without transporting matter.

This is what a wave is. But, how do we properly talk about waves? How do we compare them to one another?

### Pendulum - Wikipedia

Can we measure the size and speed of a wave? How do we know how much energy it carries? To find out, we'll need to look at the major wave parameters: We'll learn how to characterize a wave by its period, frequency, amplitude, speed, and wavelength. Once we get to know the right way to use these parameters, we'll be able to learn more about how the different waves work. These are the parts of the wave that are used to measure speed and size.

Let's start off by remembering what a wave looks like. We've seen the picture above before. It's a wave drawn over a set of X and Y axes. We plotted the wave as a function of time and said that the portion of a wave between two crests or troughs is called a wave cycle. From this image, we can see that waves travel by crests and troughs in a periodic fashion. That is, a full wave cycle always takes the same amount of time.

In this case, that amount of time is exactly two seconds.

## Wave Parameters: Wavelength, Amplitude, Period, Frequency & Speed

Two seconds is called the period of the wave. Period and Frequency The period is the time it takes a wave to complete one cycle. We measure the period in seconds, and we symbolize it with the capital letter T.

You can think of the period as the time it takes for one particle in the medium to move back and forth. If this were a water wave, all the particles in the water would be moving up and down as the wave travels through. The time it takes for one water molecule to move up, move back down, and then return to its original position, is called the period.

Knowing the period of a wave is fine, but we often need to talk about waves in terms of how often the wave cycles are coming. In other words, we want to know the frequency of a wave. A wave's frequency is the number of cycles that are completed in a certain amount of time.

**Simple Harmonic Motion, Mass Spring System - Amplitude, Frequency, Velocity - Physics Problems**

The symbol for frequency is the lowercase f, and we measure it in cycles per second, which is the same as the unit hertz.