In this experiment, you will examine the kinetic and potential energy of a mass oscillating at the end of a vertical spring. This demonstration was created at utah state university. Youll get to see how changing various parameters like the spring constant, the mass, or the amplitude affects the oscillation of the system. This will be done by measuring the position and velocity as a function of time and using the data to construct and examine graphs of kinetic and potential energies of the system. Pdf experimental study of simple harmonic motion of a spring. In the figure below, the mass and damping of the beam can be disregarded. The experimental study of simple harmonic motion of a springmass system shows that the principal physical variables that characterize the oscillations, such as k. In the springmass system only one coordinate is enough to describe the position of the mass at any time, and hence, it is single degreeoffreedom system. A spring, photogate system, and masses will be used. A mass suspended on the end of a spring bobs up and down in a regular way. To measure and investigate the dynamic characteristics of a driven springmassdamper system.
Lab 2c driven mass spring system with damping objective warning. Of primary interest for such a system is its natural frequency of vibration. The cd on the hanging mass is so that the detector can see the motion of the hanging mass. With relatively small tip motion, the beam mass approximates a mass spring system reasonably well. For the shm part of the experiment, a single mass of 4kg was hung from the spring and the time required for the system of mass plus spring to execute an integer n number of oscillations was measured with a digital stopwatch. Observe the forces and energy in the system in realtime, and measure the period using the stopwatch. Dynamics of simple oscillators single degree of freedom systems. Use equation 1 to calculate the theoretical period of the mass and spring. To measure and investigate the dynamic characteristics of a driven spring mass damper system. The theoretical period of a system composed of a mass m oscillating at the end.
Mechanical vibrations experiment the study of vibrations vibrations are oscillations of a mechanical or structural system about an equilibrium position. Suppose that a mass of m kg is attached to a spring. The springmass system is a common and easy to perform experiment often used to introduce the study of simple harmonic motions during the. For our final lab of associated with physics i, we will dissect the motions of a mass on a spri. Spring mass system an overview sciencedirect topics. The stiffness of each spring and the amount of damping can be controlled by. I am doing this experiment to find out what effect mass has on a spring.
Experimental study of simple harmonic motion of a spring. Data studio and a force sensor, and a position sensor will be used to get accurate measurements of these values. Physics lab report 2 hookes law and simple harmonic. Experimental study of simple harmonic motion of a springmass system as a function of spring diameter 43053 measure t, a mass m 0. The idea is to investigate simple harmonic oscillatory motion, observing how position, velocity and acceleration develop in time, how potential energy elastic or gravitational may be. A mass suspended on a spring will oscillate after being displaced. Spring and mass oscillations college lab experiments pasco. The mass on a spring interactive provides the user with a richlyinteractive environment for investigating the periodic motion of a mass on a spring. Vibrations are initiated when an inertia element is displaced from its equilibrium position due to an. Overview of key terms, equations, and skills for the simple harmonic motion of springmass systems, including comparing vertical and horizontal springs. Youll see how changing various parameters like the spring constant, the mass, or the amplitude affects the oscillation of the system. Start measuring by increasing the mass attached to the spring to 120 grams.
Of course, you may not heard anything about differential equation in the high school physics. For this lab, we choose to experiment with a torsional massspringdamper system. In our case the external force is determined by attaching a mass m to the end of the spring. When we neglect a mass of spring, how do we determine the each period. Introduction all systems possessing mass and elasticity are capable of free vibration, or vibration that takes place in the absence of external excitation. Place a stool under the hanger and measure the initial height x0 above the stool. Design an experiment to determine the mass of an unknown object. It is usual to obtain the effective mass by analyzing results of tm in the limit m 0. Massspringdamper systems the theory the unforced massspring system the diagram shows a mass, m, suspended from a spring of natural length l and modulus of elasticity if the elastic limit of the spring is not exceeded and the mass hangs in equilibrium, the spring will extend by an amount, e, such that by hookes law the tension in the. Sample learning goals determine the factors which affect the period of oscillation. A cantilevered beam can be modeled as a simple translational spring with indicated sti ness. This demonstration investigates the dependence of the period of the massspring system on the mass, the spring constant, and the amplitude. The objective of this experiment is to model a standard secondorder system and to investigate the effect of system parameters and feedback on its response to a step input.
The spring and damper elements are in mechanical parallel and support the seismic mass within the case. Experimental study of simple harmonic motion of a springmass. Lab 2c driven massspring system with damping objective warning. Me451 laboratory time response modeling and experimental. Springmass oscillations goals to determine experimentally whether the supplied spring obeys hookes law, and if so, to calculate its spring constant. Introduction helical or coil springs are commonly used. This experiment provides students with the possibility of. An example of a system that is modeled using the basedexcited massspringdamper is a class of motion sensors sometimes called seismic sensors. Transport the lab to different planets, or slow down time.
For example, suppose that the mass of a springmass system is being pushed or. Mass or inertia elements using mathematical model to represent the actual vibrating system e. Aug 20, 2016 this demonstration investigates the dependence of the period of the mass spring system on the mass, the spring constant, and the amplitude. This experiment provides students with the possibility of understanding the differences between theoretical models that include wellknown corrections to determine the frequency of oscillations of a springmass system.
The forced massspringdamper system consider now the case of the mass being subjected to a force, ft, in the direction of motion. A beam mass system a mass spring damper system model can be used to model a exible cantilevered beam with an a xed mass on the end, as shown below. The period of oscillation is affected by the amount of mass and the stiffness of the spring. Dynamics of simple oscillators single degree of freedom. The parametric springmass system, its connection with nonlinear. This experiment provides students with the possibility of understanding. From physics, hookes law states that if a spring is displaced a distance of y from its equilibrium position, then the force exerted by the spring is a constant k 0 multiplied by the displacement of the y. The experiment is designed to provide information on the behavior of a body hanging from a spring. We will determine the spring constant, for an individual spring using both hookes law and the properties of an oscillating spring system. Probably you may already learned about general behavior of this kind of spring mass system in high school physics in relation to hooks law or harmonic motion. Springmass systems now consider a horizontal system in the form of masses on springs again solve via decoupling and matrix methods obtain the energy within the system find specific solutions. Force constant of a spring experiment edunovus online smart. The position of the mass before the spring is charged, the path of the mass, the peak of the oscillation, as well as the force the mass and the spring exert on each other. In practice it is important to construct support systems that are stiff, compared to the deflection of the isolators, and to minimize radiation from lightweight diaphragms.
Free vibrations of a mass spring system tm164 tecquipment. The purpose of this lab experiment is to study the behavior of springs in static and dynamic situations. Add 50 g to the mass hanger and determine the change in position caused by this. Pdf the simple harmonic motion of a springmass system generally exhibits a. An undergraduate study of harmonic and parametric motion of a. A motion sensor measures the position of the oscillating mass, and the force sensor is used to determine the spring constant. Although the experimental apparatus is simple, an actual springmass system behaves as a simple harmonic. Within the experiment, in the first two parts we will determine the spring constant of a spring using two different methods. Another common misconception is that the model shown in figure 1. For an ideal system, the entire mass would be in the oscillating object, and the spring would have zero mass. Furthermore, the mass is allowed to move in only one direction. The purposes of this experiment are to measure the force constant of a spring. To determine the spring constant of a spiral spring.
For this lab, we choose to experiment with a torsional mass spring damper system. In order to find out how the spring extends we will need to add various amounts of weights to the spring. Mass, in kg, is plotted against elongation, in cm, in the graph in figure 2. In general, any system that can be modeled as mass acted on by. A beammass system a massspringdamper system model can be used to model a exible cantilevered beam with an a xed mass on the end, as shown below.
This is one of the most famous example of differential equation. Introduction helical or coil springs are commonly used in wide variety of mechanical systems. Hang the massspring system high over your lab bench and place the sonar detector above it. Force control for planar springmass running devin koepl and jonathan hurst abstractin this paper, we present a novel control strategy for springmass running gaits which is robust to disturbances, while still utilizing the passive dynamic behavior of the mechanical model for energy economy. In this lab, you will explore the oscillations of a massspring system, with and without damping. Springmass oscillations washington state university. The spring i hookes law and oscillations objectives. This experiment allows the period, displacement, velocity and acceleration to be investigated by datalogging the output from a motion sensor. Hookes law helps explain the first parts of this experiment. Then increase the mass by increments of 10 grams up to a total of 220 grams and measure the corresponding position of the spring for each mass. It is also possible to study the effects, if any, that amplitude has on the period of a body experiencing simple harmonic motion. In the third part of the experiment we will determine acceleration due to gravity by using a simple pendulum. The period of a spring was researched and the equation vfor the period is, where m is mass and k is the spring constant of an ideal spring, a value that describes the stiffness of a spring i.
The mass will of course be acted upon by gravity, so. There are two springs having diferent spring constants and there are five different masses 1kg, 2kg, 3kg, 4kg, and an unknown mass that can be hung from the spring. Massspring system an overview sciencedirect topics. The effect of mass on a spring 380 words 123 help me. To verify that this behavior is accurately described by hooks law.
Now lets add one more springmass to make it 4 masses and 5 springs connected as shown below. With relatively small tip motion, the beammass approximates a massspring system reasonably well. This experiment provides students with the possibility of understanding the differences between theoretical models that include wellknown corrections to determine the frequency of oscillations of a spring mass system. The period of oscillation is measured, and compared to the theoretical value. Finding acceleration due to gravity by oscillating massspring system. Hang the spring from the pendulum clamp and hang the mass hanger from the spring. The physics behind this simple system has widespread applicability, from electrical circuits like the tuner. Nearly undamped oscillations in this part of the lab, you will determine the angular frequency of a 170g mass 50 g for the stand, 20 g for the cd, and a 100 g mass oscillating on a long not very stiff spring. Now lets summarize the governing equation for each of the mass and create the differential equation for each of the massspring and combine them into a system matrix. Measure the position of the end of the spring after the table has been attached. It will be shown that ideally this system acts as a second order, timeinvariant system. Force control for planar springmass running devin koepl and jonathan hurst abstractin this paper, we present a novel control strategy for springmass running gaits which is robust to disturbances, while still utilizing the passive dynamic behavior of the mechanical model for. A spring mass system, used to isolate vibrating equipment from its support structure, is based on a theory that assumes that the support system is very stiff.
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