What is the uncertainty in the mass measurements? Analysis: That number will be your delta x. of the spring force equals the weight of the body, Specifically how it oscillates when given an initial potential energy. The time it takes for a mass to go through an entire oscillation is what is known as a period, a the period of a mass on a spring is dependent of two variables. and fill in the relevant information The Plumbers No fuss, affordable pricing Call us now on 1-800-000-0000 Call us now on 1-800-000-0000 Let the mean position of the particle be O. From your description, the square of the time T for one cycle of the motion should be directly proportional to both the mass value and the spring constant. Available at Ward's Science: https://www.wardsci.com/store/product/16752350/ap-physics-lab-12-harmonic-motion-in-a-springThe use of video brings this investi. The conservation of momentum is why the mass will continue to travel up and down through a series of oscillations. as you perform the experiment. 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A pendulum is a simple set up in which a string is attached to a small bob. D- Pend casing extra damping We found that the pendulum goes slower than simple pendulum theory at larger angles. Repeat that procedure for three more times and at each trial, add 20 more grams to the mass. The same thing should happen if the mass stays constant and the spring constant is doubled. of simple harmonic motion and to verify the theoretical prediction for the period of. A pendulum is a basic harmonic oscillator for tiny displacements. record in order to take data for a Hooke's Law experiment when the spring-mass Some of the examples, of physical phenomena involving periodic motion are the swinging of a pendulum, string, vibrations, and the vibrating mass on a spring. They The spring constant is an indication of the spring's stiffness. Simple harmonic motion is important in research to model oscillations for example in wind turbines and vibrations in car suspensions. By clicking Check Writers Offers, you agree to our terms of service and privacy policy. ( 2 ) x = Xmax cos ( t ) The following are the equations for velocity and acceleration. Conversely, an increase in the body's mass (1) Linear Simple Harmonic Motion: When a particle moves back and forth along a straight line around a fixed point (called the equilibrium position), this is referred to as Linear Simple Harmonic Motion. We can then determine the spring constant for this spring: Conclusion: Effects the spring constant and the mass of the oscillator have on the characteristics of the motion of the mass. obey Hooke's Law? maximum displacement Figure 5.38 (a) The plastic ruler has been released, and the restoring force is returning the ruler to its equilibrium position. We also use third-party cookies that help us analyze and understand how you use this website. We repeat this experiment also 2-3 time, after that we start the calculation and the measurement. The law is named after 17th-century . endobj . Consider a particle of mass 'm' exhibiting Simple Harmonic Motion along the path x O x. The law states that F = -ky, where F is in this case Mg and y equals the negative displacement. or the change in the position; or both? % Does the period depend on the amplitude of a pendulum? In this lab we will study three oscillating systems that exhibit nearly ideal simple harmonic motion. is the displacement of the body from its equilibrium position (at In part two of this lab, you will attach a spring on either side of a sliding mass on a frictionless air track and have a photo gate measure the period as the mass oscillates. is stretched to the 0.320m-mark as shown in Figure 4. This was shown clearly in our data. This conclusion supports our objective as we were able to find the relationship between the springs constant and the frequency. After the spring constant of 9.0312 N/m was measured, equations were used to determine a calculated frequency, that being . Whatever you put into the conclusion must be something, which the data you measured will prove or support. The cookie is set by GDPR cookie consent to record the user consent for the cookies in the category "Functional". The time required for the This was the most accurate experiment all semester. Every spring has a spring constant, this is the amount of resistance that a particular spring exerts to retain its original shape. These Science essays have been submitted to us by students in order to help you with your studies. In the first part of this lab, you will determine the period, T, of the spring by observing one sliding mass that is attached to two springs with the spring constant k, and attached to a hanging mass by a string and a pulley. The negative sign in Equation 1 indicates that the direction of Motion Lab Report Introduction Simple harmonic motion is the motion of a mass on a spring when it is subject to the linear elastic restoring force given by Hooker's Law. This cookie is set by GDPR Cookie Consent plugin. We use cookies on our website to give you the most relevant experience by remembering your preferences and repeat visits. Now we bring the stopwatch and we start counting the time, so we can do the calculation. EssaySauce.com has thousands of great essay examples for students to use as inspiration when writing their own essays. Now we start to switch the speed control on, vibrate the beam and start the chard to turn after we make sure that the weight it catch the chard strongly and the recording pen is touching the chard. the system is balanced and stable. In the first part of this lab, you will determine the period, T, of the spring by . where . That means that the force, F, is proportional to x, the distance the mass is pulled down from rest. When a mass is added to the spring it takes the length of, . c"p. for an individual spring using both Hooke's Law and the We recorded these oscillations with data studio for about 10 seconds. values. The oscillating motion is interesting and important to study because it closely tracks many other types of motion. For a small angle ( < 10) the period of a simple pendulum is given by 7-25,-(Eq. As an example, consider the spring-mass system. where frequency f the inverse of period T, f = 1 T. Therefore: 2 T = where I = (1/3)mr, so 2 T = . 1 0.20 5 20.54 17.57 0.156 19 13.45 0.34 Let the speed of the particle be 'v0' when it is at position p (at a distance x from the mean position O). Additionally, a protractor could be taped to the top of the pendulum stand, with the ruler taped to the protractor. Guidelines for a Physics Lab Reports A laboratory report has three main functions: (1) To provide a record of the experiments and raw data included in the report, (2) To provide sufficient information to reproduce or extend the data, and (3) To analyze the data, present conclusions and make recommendations based on the experimental work. Conclusions The laboratory experiment was mentioned to gain knowledge on basic parameters of the simple harmonic oscillation: period, frequency, and damping. Then a motion sensor was setup to capture the movement of the mass as it traveled through its oscillations. In this lab we want to illustrate simple harmonic motion by studying the motion of a mass on a spring. Therefore, Hooke's law describes and applies to the simplest case of oscillation, known as simple harmonic motion. Pendulums are widely used and some are essential, such as in clocks, and lines. 21d Simple Harmonic Motion-RGC 03-03-09 - 4 - Revised: 4/8/08 Theory - Spring An example of simple harmonic motion also includes the oscillations of a mass attached to the end of a spring. We will study how a mass moves and what properties of spring give the mass a predictable movement. The pendulum was released from \(90\) and its period was measured by filming the pendulum with a cell-phone camera and using the phones built-in time. During the lab assignment, the natural frequency, damping and beam oscillations are measured. In this experiment, we measured \(g=(7.65\pm 0.378)\text{m/s}^{2}\). each individual of the group. Each person in the group stretched or compressed a small distance from its equilibrium position, We will determine the spring constant, , for an individual spring using both Hooke's Law and the properties of an oscillating spring system.It is also possible to study the effects, if any, that amplitude has on the period of a body experiencing simple harmonic motion. First you must calculate the mass of the sliding mass and the equilibrium displacement of the spring. Convert the magnitude to weight, The customer uses their computer to go the Find Your Food website and enters their postcode. We thus expect that we should be able to measure \(g\) with a relative uncertainty of the order of \(1\)%. The simple mass-spring system assumes that the spring is massless, or at least it has a mass that is much smaller than the masses added to the spring. of the spring constant. Purpose. The cookie is set by the GDPR Cookie Consent plugin and is used to store whether or not user has consented to the use of cookies. This problem should be solved using the principles of Energy Conservation. In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distancethat is, F s = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring. Based on this data, does a rubber band When the body Students can use our free essays as examples to help them when writing their own work. Don't use plagiarized sources. Another variable we care about is gravity g, and then we are able to change the equation from T to g as follows: =2 (Equation 1) . , Mass is added to a vertically hanging rubber band and the displacement EssaySauce.com is a completely free resource for students. Notice that it is typed and spell checked, and should not contain errors such as interchanging "affect " and "effect". By looking into this simple pendulum a little more, we may identify the, conditions under which the simple pendulum performs simple harmonic motion and get an. 206Conclusion Sample-2004 206ConSam. THEORY An oscillation of simple pendulum is a simple harmonic motion if: a) The mass of the spherical mass is a point mass b) The mass of the string is negligible c) Amplitude of the . a) Conceptual/Theoretical Approach: This implies that table #5 working on the Ideal Gas Law experiment would rename their template file It is apparent that there is a clear relationship between an increased mass and the amount of force exerted, and consequently the amount of displacement experienced by the spring.