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The period of swing of a simple gravity pendulum depends on its length, the local strength of gravity, and to a small extent on the maximum angle that the pendulum swings away from vertical, θ 0, called the amplitude. It is independent of the mass of the bob. If the amplitude is limited to small swings, the period T of a simple pendulum, the time taken for a complete cycle, is:


The period of a simple pendulum for small amplitudes θ is dependent only on the pendulum length and gravity. For the physical pendulum with distributed mass, the distance from the point of support to the center of mass is the determining "length" and the period is affected by the distribution of mass as expressed in the moment of inertia I.


Exploring the simple pendulum a bit further, we can discover the conditions under which it performs simple harmonic motion, and we can derive an interesting expression for its period. We begin by defining the displacement to be the arc length . We see from that the net force on the bob is tangent to the arc and equals .


T is the period of oscillations - time that it takes for the pendulum to complete one full back-and-forth movement. L is the length of the pendulum (of the string from which the mass is suspended). g is the acceleration of gravity. On Earth, this value is equal to 9.80665 m/s^2 - this is the default value in the simple pendulum calculator.


A compound pendulum (or physical pendulum) is one where the rod is not massless, and may have extended size; that is, an arbitrarily shaped rigid body swinging by a pivot. In this case the pendulum's period depends on its moment of inertia I around the pivot point. The equation of torque gives: = where:


The period for a simple pendulum does not depend on the mass or the initial anglular displacement, but depends only on the length L of the string and the value of the gravitational field strength g, according to The mpeg movie at left (39.5 kB) shows two pendula, with different lengths.


• Time period of simple pendulum motion: The time taken by the pendulum to complete one full oscillation is called the time period of oscillation. It is denoted by the symbol "T". • Amplitude of simple pendulum motion: The distance traveled by the pendulum from the equilibrium position to one side is called the amplitude of oscillation of ...


A simple pendulum is defined based on the motion which repeats itself at a regular time interval known as the time period of a simple pendulum. To know more on the derivation of the time period of the pendulum, please visit BYJU’S.


A mass m suspended by a wire of length L is a simple pendulum and undergoes simple harmonic motion for amplitudes less than about 15º. The period of a simple pendulum is [latex]T=2\pi\sqrt{\frac{L}{g}}\\[/latex], where L is the length of the string and g is the acceleration due to gravity.


Equation (8) shows that the acceleration a of the bob is directly proportional to the displacement x and negative sign shows that it is directed towards the mean position.Hence the motion of simple pendulum is simple harmonic. Time period of simple pendulum. The acceleration of the body is given by: