# Kinetic Analysis – Math Problem Example

Introduction The main aim of this paper is to develop and simulate double mass spring damper in Matlab simMechanics. Graphs will be made for the results showing changes in various parameters and the results highlighted. In designing double mass damper Hooke’s law will be applicable. RationalThe rational of this paper is to design double mass spring damper as shown in the diagram below with the intention of creating a model that will show the impact of changing the stiffness of the spring and damping coefficient. The model will have two masses, two spring constants, and two damping coefficients.

The masses will be held by springs whose weight will be ignored. It will be assumed that force will be exerted by external force and there will be displacement. The following are damping coefficients, mass and spring constants. Figure 1: double mass spring damperfind the natural frequencies and mode shapes of spring mass system, which is constrained to move in the vertical direction. Solution: the equations of motion are given by: Validation The double mass spring damper will be done in both excel and in Matlab Simulink using the same parameters.

Figure 2 shows Simulink model that has been built. The Simulink model is a closed-Loop Response Figure 2:: Block diagram The solution to above kinematical parameters for individual members of model Hooke’s law will be applicable. According to Hooke’s law the displacement of the ideal spring is proportional to the force exerted that is the deformation-change in size or shape-of the object is proportional to the magnitude of the force that causes the deformation. The extension or compression-the increase or decrease in length from the relaxed length-is proportional to the force applied to the ends of the spring.

The assumption is that springs mass is ignored. The springs have constant k is called the spring constant for a particular spring as shown above diagram of 40500 N/m. the spring constant is a measure of how hard it is to stretch or compress a spring. A stiffer spring has a larger spring constant because larger forces must be exerted on the ends of the spring to stretch or compress it. It can be noted that second mass has a wave that is stable while the first mass has its wave not being stable.

Stable waves occur when a wave is reflected at a boundary and the reflected wave interferes with the incident wave so that the wave appears to stand still. Suppose that a harmonic wave on a string, coming from the right, hits a boundary where the string is fixed. The equation of the incident wave is . The +sign is chosen in the phase because the wave travels to the left.

The reflected wave travels to the right, sois replaced with and the reflected wave is inverted, so is replaced with. Then the reflected wave is described by, the motion of the string is described by ], Thus. Where and Every point moves in second mass with the same frequency as compared first mass due impact of the force. However, in contrast to first mass where every point does reaches its maximum distance from equilibrium simultaneously. In addition, different points moves with different amplitudes; the amplitude at any point is