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Also notice that the position of the pendulum, anything on the right from its original position i.e. It takes another 1 second to reach back to the position it started. We will notice that it takes 2 seconds to reach the maximum height of -15cm towards the left side of the equilibrium point. When we pull the pendulum to the right, the position of the pendulum before we release it is 15 cm at Time (t) =0. When we pull the pendulum to the right so that it displaces 15 cm and then release so that it oscillates that is moving back and forth. Let’s take the example of the pendulum in which we will measure oscillation that measures different positions of the pendulum and the time it takes to reach these positions. Harmonic graphs mathematical or logical models to plot harmonic motions or harmonic series. Trick here is whenever you are given Harmonic Progression convert it into A.P Example:įind the next four terms of the sequence: - 1/7, -1/2, -1/11 …. So, the difference between the 1st and 2nd fraction in the sequence is 2/3 and the same is the case with 2nd and 3rd fraction or 3rd and the 4th. So, the A.P of the above sequence can be expressed as And the sum of this sequence would be a harmonic series. Now if we prove that the reciprocal of the above sequence is A.P with a common difference then we can establish that the sequence is the Harmonic sequence.
What is a harmonic series#
We have to determine if the below series is Harmonic series or not The Harmonic Sequence of the above Arithmetic Sequence is If we have Arithmetic Sequence as 4,6,8,10,12 with the common difference of 2 And the sum of such a sequence is known as Harmonic Series Example The reciprocal form of the Arithmetic Sequence with numbers that can never be 0 is called Harmonic Sequence. Here we will understand every concept of Harmonic Series following the Arithmetic sequence. I assume you all have already covered Arithmetic Progression under Sequence and Series. Before we understand Harmonic Sequence or Harmonic Series, we must understand what is Arithmetic sequence /Arithmetic Progression.