The Second’s Pendulum

A weight being suspended from a pivot for it to swing freely is known as a pendulum. Normally it stays in an equilibrium position before getting displaced in a sideward manner. A pendulum is a subject which restores force due to gravity of the earth allowing the pendulum to return back to the equilibrium position using the gravitational acceleration. On getting released it starts to oscillate around the equilibrium position as a result of the resting force’s action on the mass of the pendulum. Time period of pendulum is the total time required to complete 1 whole oscillation . A whole oscillation involves a left swing and a right swing. There are a few factors affecting the period of the pendulum, the factors are:-

• Length of the pendulum.
• Amplitude
• Width of the swinging pendulum.

Time period formula of a pendulum The time period formula (T) of a pendulum is T = 2π √L/g ,here L denotes the length of the pendulum and g denotes the acceleration due to gravity. The formula says the time period of pendulum is equal to two π multiplied by the square root of L divided by g.

History of second pendulums

A Dutch scientist named Christiaan Huygens had invented the pendulum clock in 1656 . He later patented the pendulum in 1657 . The clock design was assigned to Salomon Coster. He used a second’s pendulum for the clock. During 1602 Galileo Galilei had conducted and published some investigations of pendulums and Huygens took inspiration from it. Galileo had discovered many new properties of the pendulum. One of them was isochronism and it meant that even if the swings are of different sizes the period would stay the same. Moreover, in 1637 Galileo already had the idea of the pendulum clock. His son constructed the clock in 1649 but it couldn’t be finished. The accuracy of the clocks was on the rise with the use of pendulums in them. Wide results ranging from 15 minutes to 15 seconds on a daily basis.

Types of pendulum

There are mainly three broad types of pendulum which are :-

• Simple pendulum – It is the most common version of a pendulum we know. It is made up of a weight attached and hanging at the end of a string . Clocks frequently use these pendulums in them. Due to some variations in the gravitational pull of the earth, pendulums may work differently in different parts of the world. It is seen according to studies pendulum swings are slower near the equator than the poles.
• Foucault pendulum – It is a pendulum which has the capability of swinging in two dimensions. Jean Bernard Leon Foucault was the one to develop this pendulum in 1852 and he also showed the rotation of the earth using the pendulum. When it is moved and brought into movement it swings by rotating in clockwise circular motion for more than a day.
• Double pendulum – It is a combination of two simple pendulums. First is normally suspended and the second pendulum is suspended from the first pendulum. It is known as a chaotic pendulum too because small motion happens normally but with the increase of unpredictability. The second pendulum experienced unusual movement.

The formula for the second’s pendulum If an object with mass is on a weightless string with nearly negligible amplitude, without any resistance then:- Let, The length of the string be L L=g/π² Here g is the acceleration due to gravity. These are in SI units. Therefore, we can say that the value of g is 9.80665 m/s2 . The L will be 993.6 millimetre. This is just 1cm short of being one metre. The value of g is expressed in this unit as it is very close to π² .

Conclusion

Pendulum was a very necessary discovery for not the field of science but for our daily usage too , pendulum clocks had become staple at every household at one point. Mainly the second’s pendulum helped in discoveries such as finding the shape of the earth which was conducted by Sir Isaac Newton.