 is one type of mechanical shock occurring so often that many studies have been made of its effects on equipment. The nature of this impact is written in its shock signature, a record of acceleration as a function of time. A different shock signature is produced by this unfortunate but common transportation incident and this kind of transportation shock lights a still different signature. Some equipment such as vital gear aboard a submarine must not only survive normal transportation shocks and still operate but such equipment must also work properly while actually under attack. To design and test equipment which will operate under severe conditions the engineer must properly interpret the shock signature and then accurately predict the effects of the shock on the equipment that is the equipment's response to mechanical shock. This film develops the concept of shock response spectra and illustrates how the engineer can use shock response spectra in the design and testing of equipment. The film reviews the basic parameters used to define shock, acceleration, velocity and displacement and shows their interdependence. The concept of the spring mass model is reviewed and the development of shock response spectra from the spring mass models is illustrated. The film also shows how the analysis of complex systems can be approached by computer calculation of shock response. First let's review the parameters used to describe mechanical shock, acceleration, velocity and displacement. Let's assume that a rigid body is at rest, no velocity, no displacement from a reference position. Acceleration of the body is its change of velocity with time. We see a constant acceleration starting at zero and continuing for a certain amount of time. This is followed by constant acceleration in the opposite direction and by additional constant acceleration in the original direction returning to zero again. What happens to velocity? Velocity you remember is the change of displacement with time measured from the fixed reference point. Now we see the velocity changes which result from the acceleration shown before. The cumulative area under the acceleration curve will give us velocity at any time. If the initial velocity and a time history of acceleration are known, the time history of the velocity can be obtained and last displacement defined as the magnitude of movement of a body from the reference point. We see the displacement change which results from the velocity shown before. The cumulative area under the velocity curve will give us the displacement at any time. Therefore, if the initial displacement and a time history of velocity are known, the time history of the displacement can be obtained. These examples illustrate that the functions of acceleration, velocity, and displacement are interdependent. In the case of truly rigid bodies, knowledge of acceleration, velocity, and displacement would allow appropriate design calculations to be made. However, bodies which are apparently rigid actually react to force in an elastic manner, causing relative motion between different regions. This results in different accelerations, velocities, and displacements which are difficult to analyze. To approximate the motion of an elastic body, the engineer may substitute an equivalent spring mass model. The simplest spring mass model is the single degree of freedom system. This includes a base to which a spring is attached, supporting a mass. The mass is free to move in one axis only, and therefore is called a single degree of freedom system. Force suddenly applied to the base of the spring mass model will cause the mass to oscillate at the natural frequency of the system. The system will continue to oscillate until some opposing force is introduced, such as this small damper, which causes the system to come slowly to rest. An example of underdamping, a large amount of damping, overdamping, causes the mass to return slowly to its neutral position without oscillating. Critical damping is that amount which causes the mass to return to equilibrium in the shortest time without oscillating. The effects of different amounts of damping are illustrated with this swinging door. A concealed spring closes the door, but the damping device causes the door to close too slowly overdamping. The amount of damping can be reduced, but now the door swings too freely underdamping. Another change to increase the damping action. With the proper amount of damping, the door opens easily, yet closes quickly, without overshooting the closed position. Critical damping. Let's look at the effects of suddenly applied force on spring mass systems with no damping. In this case, the rocket body is the base of the system. When the acceleration amplitude of the input pulse, the rocket motor is constant. Acceleration and displacement responses of the mass are influenced by the duration of the input pulse. A short live pulse, much shorter than one complete oscillation of the mass at its natural frequency, will cause relatively small acceleration of the mass with respect to the base. The sine wave represents the amplitude of the acceleration of the responding mass. An acceleration pulse of the same amplitude, but having a longer duration, will produce correspondingly greater acceleration of the mass with respect to the base. Even though the amplitude of the acceleration increases, the frequency of the motion remains the same. The sine wave again shows the acceleration response of the mass. An even longer input pulse, the duration of which is nearly as long as the time of one oscillation of the mass, will produce still greater acceleration. For square impulses like these, the maximum acceleration upon the mass will be no more than twice the acceleration input to the base. Longer input acceleration forces of the same amplitude will not increase the acceleration of the mass beyond this maximum value, as shown again by the sine wave. In other words, for square pulses of given amplitude, the response of the spring mass system increases with longer pulses, up to a maximum acceleration of twice the value of the input pulse. Up to this limit, however, maximum acceleration is a function of pulse duration. Damping in this spring mass system would reduce the acceleration response for a simple pulse. As we have seen, an undamped spring mass system will oscillate at its natural frequency. But what will be the effect of substituting different springs and then subjecting the spring mass systems to identical input forces? Changing the springs will change the natural frequencies of the systems and will therefore alter the acceleration responses of the mass. The sine wave indicates the rising frequency and shows the increasing amplitude of the acceleration responses. Notice that as the springs become stiffer, with the resulting higher natural frequency, the acceleration becomes greater. The maximum acceleration of the mass is plotted as a function of the natural frequency of each of the three spring mass systems. Now let's add more springs and then subject each resulting spring mass model to the same square pulse. A plot of maximum acceleration of the mass as a function of the natural frequencies of the spring mass systems produces this curve, which is the shock response spectrum for the square pulse. The same procedure is repeated for a complex input, rather than for a square pulse. The maximum acceleration of the mass is plotted as a function of the natural frequencies of many spring mass systems. The result is the shock response spectrum for this complex shock input. The difficult and time-consuming chore of calculating and plotting this type of shock response spectrum is performed quickly by modern computers and high-speed plotters. One of the computer inputs is the shock signature, the record of acceleration versus time. This is the forcing function which all the single degree of freedom systems experienced. The computer was programmed to calculate maximum response to this forcing function for systems with natural frequencies ranging from 10 to 10,000 cycles per second or Hertz. The three plots show the effects of typical damping ratios found in equipment. Such shock response spectra are tools which the engineer can use in several ways. When the engineer can approximate his design with a single degree of freedom system, the shock response spectrum will show the frequency at which maximum acceleration occurs, as well as its magnitude. Studying the shock spectra may suggest to the engineer that he beef up the design or change the damping, so the equipment will withstand the indicated acceleration, or he may change the spring rate or the mass of his equipment, so the natural frequency moves to an area where smaller response accelerations occur. Another use of shock spectra is in testing. A shock test using railroad cars might cost several thousand dollars, but equivalent tests conducted in the laboratory will cost much less and have the advantage of repeatability under controlled conditions. The variables of live testing are thereby eliminated. The shock testing equipment generates repeatable, simple shock inputs. The shock spectrum of the laboratory test can be compared to the shock spectrum from the actual environment in order to select a laboratory test. The lab test will cause approximately the same responses in the equipment as the field test would produce. In this case, the engineer is fitting the normalized HeverSign pulse spectrum over the response spectrum from the field test. He chooses 3% damping as representative of his equipment. He reads the amplitude required from the response G scale of the field test shock response spectrum. He also reads the frequency appearing opposite the index and calculates the duration of the lab test pulse, which is the reciprocal of the frequency. Relatively, simple components can be considered by the engineer as being single degree of freedom systems. However, equipment is quite often made up of many components which interact with each other during shock. Shock response spectra are of limited use in analyzing such complex shock problems, and these multiple degree of freedom systems require more rigorous analysis. A multiple degree of freedom system is shown in this animated drawing. Each center of mass is connected to its neighbor by a spring, making the entire structure a series of masses and interconnecting springs. Therefore, four supplied to any part of the structure will be transmitted in a rather complex manner throughout the system. In such systems, the calculation of shock responses for all possible combinations of frequencies is too time-consuming for practical design work. However, when the engineer assigns values to each mass and each spring, the shock response of each mass can be calculated by solving the equations of motion. The responses to a known shock signature of a system having more than 100 different masses and interconnecting springs can be derived through the use of available computer programs. For any input shock, the engineer must know the shock response of his equipment. For simple systems, conceived as being single degree of freedom systems, the response spectrum is the best tool for designing and testing shock-resistant equipment. For multiple degree of freedom systems, computers make possible the rapid calculation of shock response. These methods are the designer's tools for determining response to mechanical shock.