Mass-Spring Mechanism

This may be defined as the oscillatory movement of a mechanical system, and it may be sinusoidal or non-sinusoidal (also known as complex). Vibration can occur in many modes, and the simplest is the single freedom-of-movement system. A mass/spring diagram (Figure 42.7) can explain the vibration of a system. 

If the input frequency is low, the response of an oscillatory system will almost duplicate the input At the higher frequencies the response will depend on the ratio of actual damping c to critical damping c,. For the electrical system critical damping is 2 JlTC for the mechanical mass-spring-damper system the critical damping is ijkm, where... 

The classic method for source modelling mentioned in the introduction to this chapter is embodied by physical modelling techniques. Physical modelling emulates the behaviour of an acoustic device using a network of interconnected mechanical units, called mass-spring-damping, or MSD units (Figure 4.13). On a computer, this network is implemented as a set of differential equations, whose solution describes the waves product by the model in operation. Sound samples result from the computation of these equations. 

Apart from reducing the reflected mechanical impedance of a robot in order to make the mechanics sensitive , the design of interaction control schemes is an essential step for sensitive force exchange with the environment. The most widely used control approach to physically interact with robots is probably impedance control and its related schemes, introduced in the pioneering work of Neville Hogan [19] and extended to flexible joint robots in [7,2,26,3,20]. This type of controller imposes a desired physical behavior with respect to external forces on the robot. For instance the robot is controlled to behave like a Cartesian second order mass-spring-damper system, see Fig. 2. 

Fig. 2. Desired mechanical behavior expressed by mass-spring-damper...

The mass-spring system of the vertical seismometer serves as a very useful model for understanding the basics of seismometry. However, in practical design, this system is too simple, since the mass can move in all directions as well as rotate. So, nearly all seismometers have some mechanical device which will restrict the motion to one translational axis. Figure 5 shows how this can be done in principle for a vertical seismometer. 

The hamionic oscillator (Fig. 4-1) is an idealized model of the simple mechanical system of a moving mass connected to a wall by a spring. Oirr interest is in ver y small masses (atoms). The harmonic oscillator might be used to model a hydrogen atom connected to a large molecule by a single bond. The large molecule is so... 

Materials and Reactions. Candle systems vary in mechanical design and shape but contain the same genetic components (Fig. 1). The candle mass contains a cone of material high in iron which initiates reaction of the soHd chlorate composite. Reaction of the cone material is started by a flash powder train fired by a spring-actuated hammer against a primer. An electrically heated wire has also been used. The candle is wrapped in insulation and held in an outer housing that is equipped with a gas exit port and rehef valve. Other elements of the assembly include gas-conditioning filters and chemicals and supports for vibration and shock resistance (4). 

This relationship characterizes the mechanical sensitivity of the vertical spring balance, because it shows the change in displacement due to a change in the field and the ratio mjk is the parameter of this sensitivity. It is clear that with an increase of this ratio in principle, we are able to observe smaller changes of the field because the difference A/ becomes larger. This dependence of m and k is almost obvious. For instance, with an increase of mass the gravitational force increases and a greater... 

Mechanical sensitivity and stability of vertical spring-mass system... 

The vertical spring and mass is an example of a stable system and by definition this means that an arbitrary small external force does not cause the mass to depart far from the position of equilibrium. Correspondingly, the mass vibrates at small distances from the position of equilibrium. Stability of this system directly follows from Equation (3.102) as long as the mechanical sensitivity has a finite value, and it holds for any position of the mass. First, suppose that at the initial moment a small impulse of force is applied, delta function, then small vibrations arise and the mass returns to its original position due to attenuation. If the external force is small and constant then the mass after small oscillations occupies a new position of equilibrium, which only differs slightly from the original one. In both cases the elastic force of the spring is directed toward the equilibrium and this provides stability. Later we will discuss this subject in some detail. 

The theory behind molecular vibrations is a science of its own, involving highly complex mathematical models and abstract theories and literally fills books. In practice, almost none of that is needed for building or using vibration spectroscopic sensors. The simple, classical mechanical analogue of mass points connected by springs is more than adequate. 

This P -I type of response curve can also be easily shown to apply to a simple rigid-plastic mechanical system, in the manner shown in Figure 16 (see Refs. 15 and 22). Here, the spring in the system is replaced with a pure Coulomb friction element, with resisting force f, which is independent of displacement once the mass starts to move. All other symbols are defined above. 

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