# Pendulum length and frequency relationship

### The Simple Pendulum To understand the relationship between gravitational forces and the mass of ( The frequency is the number of back and forth swings in a certain length of time.) . the frequency 'ƒ' of the oscillation is the number of oscillation simple pendulum The period of a simple pendulum of constant length is independent of its mass, the relationship between the period and the length of a simple pendulum to. Pendulum motion was introduced earlier in this lesson as we made an attempt to understand the nature of vibrating .. There is a direct relationship between the period and the length. . Which would have the highest frequency of vibration?.

Questions you may have include: What are the factors and parameters of pendulum motion? What are the equations for frequency and period?

## Exploring Pendulums

What are the equations for the length of the pendulum string? This lesson will answer those questions. Units Conversion Factors and parameters The major factor involved in the equations for calculating the frequency of a simple pendulum is the length of the rod or wire, provided the initial angle or amplitude of the swing is small.

The mass or weight of the bob is not a factor in the frequency of the simple pendulum, but the acceleration due to gravity is a factor. This means that the frequency and period would be different on the Moon versus on the Earth.

Knowing the length of the pendulum, you can determine its frequency. Or, if you want a specific frequency, you can determine the necessary length.

### Equations for a Simple Pendulum by Ron Kurtus - Physics Lessons: School for Champions

Factors and parameters in a simple pendulum See Demonstration of a Pendulum to see a pendulum in motion Period equation The period of the motion for a pendulum is how long it takes to swing back-and-forth, measured in seconds. 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 avoids the friction and 'play' caused by a pivot, and the slight bending force of the spring merely adds to the pendulum's restoring force. A few precision clocks have pivots of 'knife' blades resting on agate plates. The impulses to keep the pendulum swinging are provided by an arm hanging behind the pendulum called the crutch, ewhich ends in a fork, f whose prongs embrace the pendulum rod. The crutch is pushed back and forth by the clock's escapementg,h.

Each time the pendulum swings through its centre position, it releases one tooth of the escape wheel g.

Time Period of a Pendulum - How Does it Depend on its Length?

The force of the clock's mainspring or a driving weight hanging from a pulley, transmitted through the clock's gear traincauses the wheel to turn, and a tooth presses against one of the pallets hgiving the pendulum a short push. The clock's wheels, geared to the escape wheel, move forward a fixed amount with each pendulum swing, advancing the clock's hands at a steady rate.

### Pendulum Motion

The pendulum always has a means of adjusting the period, usually by an adjustment nut c under the bob which moves it up or down on the rod. Some precision clocks have a small auxiliary adjustment weight on a threaded shaft on the bob, to allow finer adjustment. Some tower clocks and precision clocks use a tray attached near to the midpoint of the pendulum rod, to which small weights can be added or removed.

This effectively shifts the centre of oscillation and allows the rate to be adjusted without stopping the clock.

## Equations for a Simple Pendulum

Pendulum clocks should be attached firmly to a sturdy wall. The most common pendulum length in quality clocks, which is always used in grandfather clocksis the seconds pendulumabout 1 metre 39 inches long. Only a few large tower clocks use longer pendulums, the 1. The wood had to be varnished to prevent water vapor from getting in, because changes in humidity also affected the length.