TOWARDS THE PERFECT CLOCK

To measure time, we need some periodic motions. The sun rises and sets regularly. This periodic phenomenon used to measure time in those days. Sun dial was constructed and the shadow was used to indicate time. We know, the sun's apparent motion is not accurately periodic.

Then Galileo discovered the pendulum. The time taken by the pendulum for the oscillations does not depend on the mass suspended or the length of the swing but only depends on its length. A "one meter" (99 cm) long pendulum takes 2 seconds for an oscillation. So people constructed pendulum clocks which showed time for 270 years successfully.

Next came, quartz crystal based clocks. When a tiny electrical voltage is given to a tiny fork like crystal, perfect vibrations are set in it. Exactly 32768 times a second. This precise frequency is the basis for measuring the second and the time. This electronic clock is definitely more accurate than pendulum and other mechanical clocks.

We know,sodium lamp (sodium atoms) emit yellow light. The Frequency of yellow light is 5.17*10^14. That is, the sodium atom emits 5.17*10^14 light waves in one second.
Similarly caesium atom emit 9192631770 microwaves in one second. This frequency mostly accurate. So atomic clocks were constructed using caesium. Today "one second" is defined using frequency of waves emitted by caesium atom. Atomic clock is the gold standard for today"s time measurements.

But physicists say that even atomic clocks are not accurately accurate. Only clocks based on the Speed of light can be absolutely accurate because the speed of light is fundamental universal constant. And all other physical quantities will at least suffer micro changes in the course of time.

How to make that"Light Clock". Take two plane mirrors.keep them parallel at some distance apart.We know, mirrors reflect light rays. Let a light ray travel to and fro between the mirrors. In other words, let light photons bounce and re bounce between the mirrors. This is the periodic motion.
Time taken for to and fro travel by the photons is an absolute constant since the light's velocity is constant. If a clock is built using this concept, that will be the world's perfect clock. That clock will not only measure the time with great precision but will also define the time itself. The "light-clock" is not built so far. but one day, we will make that zero-error clock.

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LISSAJOUS FIGURES

Definition: "When a particle is subjected to two sine wave motion or two oscillatory motion at right angles, the particle describes lissajous figures". We know sine wave motion and circular motion is basically same. Hence we draw two circles A and B perpendicular to each other. The circle B rotates twice faster than circle A. That is, frequency of circle B is two times than that of A. A particle at the intersection of two circles is subjected to two sine wave motion A and B at 90 degree simultaneously. The particle will describe figures depending on the frequency and phase of A and B . In our case, the ratio of frequency is 1:2 and the two waves are in phase. To draw lissajous figures : A moving point in both the circles are chosen. Here we should remember; during the time taken by the circle A to complete one rotation, circle B completes two. Hence the points are marked on the circles according to their speed. Then straight lines

THE PARABOLA

A jet of water shooting from a hose pipe will follow a parabolic path. What is the so special about parabola. Y= x^2 Draw a graph for the above equation. It will result in a parabola. This parabola is also called unit parabola. Any equation involving square will yield a parabola. Example: Y = 2x^2 +3x+3 (also called quadratic equation) X= 2 and -2, both satisfies the equation 4 = X^2. Parabolic equations always have two solutions. Any motion taking place freely under gravity follows parabolic path. Examples: An object dropped from a moving train, A bomb dropped from flying plane, A ball kicked upwards. If a beam of light rays fall on the parabolic shaped mirror, they will be reflected and brought to focus on a point. This fact is made use of in Dish Antenna, Telescope mirrors, etc. Inverted parabola shape is used in the construction of buildings and bridges. Because the shape is able to bear more weight. A plane

CASINO'S GAME

Let us find out how the casino survives with mathematics. Say, your friend invite you for a game of dice. You must bet (wager) 2 dollars. If you roll 'six' you will get back 8 dollars. The game will go on for 30 rounds. All sounds good. The probability of rolling 'six' is 1/6. Since the game will be played for 30 times, the 'expected win' is 30*1/6 = 5. That is, you are expected to win 5 rounds out of 30. Hence your gain will be 5 * 8 =40 dollars. ok. This also implies that you will loose 25 rounds. Hence your loss will be 25*2 =50 dollars. Your net gain will be gain-less = 40-50 = -10 dollars. For 30 rounds, the loss is -10 dollars, Hence, for one round =-10/30 = -1/3 dollars. There will be a loss of -1/3 or 0.33 dollars per round. It is not a fair game. Let us make a simple formula to calculate 'Pay out per round\. The probability for a win = p The pay-out in case of win = V No. of rounds = n The expect

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