Each seismograph records the times when the first (P waves) and second (S waves) seismic waves arrive. To determine the direction each wave traveled, scientists draw circles around the seismograph locations. The radius of each circle equals the known distance to the epicenter.

By looking at the amount of time between the P and S wave on a seismogram recorded on a seismograph, scientists can tell how far away the earthquake was from that location. Scientists then use a method called triangulation to determine exactly where the earthquake was (see image below).

A seismograph produces a graph-like representation of the seismic waves it receives and records them onto a seismogram. This animation shows how distance is determined using P, S, and surface waves. The scientist then draws a circle with a radius equal to the distance from the epicenter for that seismograph.

One seismic station can give information about how far away the earthquake occurred, but yields little other information. The cartoonish amplified ground motions show the compressive P wave, the shearing S wave, and the rolling surface wave motions recorded by many stations with their characteristic seismograms.

P waves

Seismometers measure motions of the ground, including seismic waves generated by earthquakes, nuclear explosions, and other seismic sources.

Three seismographs

The time taken by the wave to complete one cycle of motion is called period of the earthquake wave. In general, earthquake shaking of the ground has waves whose periods vary in the range 0.03-33sec. Even within this range, some earthquake waves are stronger than the others.

At a high level, the responsibilities naturally lie with the person who will suffer loss in a disaster, which is ultimately the client, asset owner or tenant. However, the quality of construction, and therefore the seismic design, is regulated through federal, state and local governments.

Real structures are multi-degree-of freedom systems, and have several vibration modes, each with its own period of vibration. The mode with the longest period is called the fundamental period or natural period. High frequency loads such as walking or exercise (1 Hz – 3 Hz) can resonate with floor systems.

According to periodic function definition the fundamental period of a function can be defined as the period of the function which are of the form, f(x+k)= f(x) f(x+k)=f(x), then k is known as the period of the function and the function f is known as a periodic function.

This is the precise definition of “period”. The period formula, T = 2π√m/k, gives the exact relation between the oscillation time T and the system parameter ratio m/k.

The period of a function f(x) is p, if f(x + p) = f(x), for every x. A function is said to be periodic if its value repeats after regular periods (intervals). The formula is Period, P = Period of parent function/ |Coefficient of x|

The period is the time it takes for an oscillating system to complete a cycle, whereas the ​frequency (​f​)​ is the number of cycles the system can complete in a given time period. For example, the Earth rotates once each day, so the period is 1 day, and the frequency is also 1 cycle per day.

Period refers to the time for something to happen and is measured in seconds/cycle.

The period of the object’s motion is defined as the time for the object to complete one full cycle. Being a time, the period is measured in units such as seconds, milliseconds, days or even years. The standard metric unit for period is the second. An object in periodic motion can have a long period or a short period.

The period of a pendulum does not depend on the mass of the ball, but only on the length of the string. Two pendula with different masses but the same length will have the same period. Two pendula with different lengths will different periods; the pendulum with the longer string will have the longer period.

Types of Motion

• Rectilinear motion,
• Circular motion,
• Periodic motion and.
• Rotational motion.

Since simple harmonic motion is a periodic oscillation, we can measure its period (the time it takes for one oscillation) and therefore determine its frequency (the number of oscillations per unit time, or the inverse of the period).

That is, F = −kx, where F is the force, x is the displacement, and k is a constant. This relation is called Hooke’s law. A specific example of a simple harmonic oscillator is the vibration of a mass attached to a vertical spring, the other end of which is fixed in a ceiling.

Graph of displacement against time in simple harmonic motion. where F is force, x is displacement, and k is a positive constant. This is exactly the same as Hooke’s Law, which states that the force F on an object at the end of a spring equals -kx, where k is the spring constant.

each complete oscillation, called the period, is constant. The formula for the period T of a pendulum is T = 2π Square root of√L/g, where L is the length of the pendulum and g is the acceleration due to gravity.

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 T=2π√Lg T = 2 π L g , where L is the length of the string and g is the acceleration due to gravity.

The tangential acceleration = radius of the rotation * its angular acceleration. It is always measured in radian per second square. Its dimensional formula is [T-2].

Equations

Equation	Symbol breakdown
v = r ω v = r /omega v=rω	v v v is linear speed, r is radius, ω is angular speed.
T = 2 π ω = 1 f T = /dfrac{2/pi}{/omega} = /dfrac{1}{f} T=ω2π=f1	T T T is period, ω is angular speed, and f is frequency

Three Equations of Motion are v = u + at; s = ut + (1/2) at² and v² = u² + 2as and these can be derived with the help of velocity time graphs using definition acceleration.

Uniform circular motion can be described as the motion of an object in a circle at a constant speed. As an object moves in a circle, it is constantly changing its direction. An object undergoing uniform circular motion is moving with a constant speed. Nonetheless, it is accelerating due to its change in direction.

The movement of a body following a circular path is called a circular motion. Now, the motion of a body moving with constant speed along a circular path is called Uniform Circular Motion. Here, the speed is constant but the velocity changes.