This was the most accurate experiment all semester. . is the known as the spring constant, and It was, found that a longer pendulum length would result, in a longer period and that the period of the, pendulum was directly proportional to the square, root of the its length. We will determine the spring constant, P14: Simple Harmonic Motion - Mass on a Spring 012-07000A p. The block is released, follows the trajectory shown, and strikes the floor a horizontal distance D from the edge of the table. Available from: [Accessed 04-03-23]. Show the following calculations using the trendline fit equation from the Excel graph of Part 1: The spring constant k = 472 x 0.3304 = 13.04 N/m The uncertainty in the spring, Data and Analysis Part A: Finding the inverse of one vector Make a prediction of the correct weight and direction to balance the given force. . Then when the spring is charged with additional potential energy, by increasing the length to where can also be defined as the spring will exert whats called a restoring force which is defined as where is a spring constant. to some final position, We will be recording basic information. During the lab assignment, the natural frequency, damping and beam oscillations are measured. 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. Course Hero is not sponsored or endorsed by any college or university. In other words, the spring We reviewed their content and use your feedback to keep the quality high. The same thing should happen if the mass stays constant and the spring constant is doubled. 4: Chard recorder (a slowly rotation drum with a paper roll moving at constant speed) 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. In this lab, we will observe simple harmonic motion by studying masses on springs. What is the uncertainty in the period measurements? We will study how a mass moves and what properties of spring give the mass a predictable movement. Group 5. the spring force is a restoring force. Extension: Have students repeat their procedure using two springs in series and two springs in parallel with the same masses . If the body in Figure 4 is displaced from its equilibrium position some The body A pendulum is a basic harmonic oscillator for tiny displacements. The corresponding value of \(g\) for each of these trials was calculated. The IV of our experiment was the changes in the mass we made, the DV was the outcome of the frequency, and the constants were the type of spring we used as well as the amplitude. The site offers no paid services and is funded entirely by advertising. In order to minimize the uncertainty in the period, we measured the time for the pendulum to make \(20\) oscillations, and divided that time by \(20\). where this force exists is with a common helical spring acting on a body. Purpose. This sensor was set to a frequency of . 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. When block away when the subject of stability or the balance spring will exert force to return it back to the original position. we say that the mass has moved through one cycle, or oscillation. If the block has not lost its capacity will continue to vibration, so they patrol movement is repeated every period of time and then well show it Simple harmonic motion. EssaySauce.com is a completely free resource for students. CALIFORNIA STATE UNIVERSITY, LOS ANGELES Department of Physics and Astronomy Physics 212-14 / Section 14- 34514 Standing waves On Strings Prepared by: Faustino Corona, Noe Rodriguez, Rodney Pujada, Richard Lam Performance Date: Tuesday,April 6, 2016 Submission Due: Tuesday, April 13, 2016 Professor: Ryan Andersen Wednesday: 6:00 pm. The objective of this lab is to understand the behavior of objects in simple harmonic motion by determining the spring constant of a spring-mass system and a simple pendulum. the spring force acting on the body. , A pendulum is a simple set up in which a string is attached to a small bob. Equation 1: F = kx F = k x. F is the restoring force in newtons (N) k is the spring constant in newtons per meter (N/m) x is the displacement from equilibrium in meters (m) When you add a weight to a spring and stretch it then release it, the spring will oscillate before it returns to rest at its equilibrium position. Here the constant of proportionality, Then a motion sensor was setup to capture the movement of the mass as it traveled through its oscillations. A simple pendulum consists of a small-diameter bob and a string with a tiny mass but, enough strength to not to stretch significantly. However, you may not have changed the spring constant, and if you didnt change it and measure what happened to the time T when you did, you cannot put that proportionality into your conclusion. The potential energy is a not only a controled by the initial forced change in displacement but by the size of the mass. It was concluded that the, mass of the pendulum hardly has any effect on the, period of the pendulum but the length on the other, hand had a significant effect on the period. This cookie is set by GDPR Cookie Consent plugin. Does the value of the oscillation amplitude affect your results? Necessary cookies are absolutely essential for the website to function properly. and counted the cycles, and the last partner had timed the process. It is also possible to is the displacement of the body from its equilibrium position (at body to complete one oscillation is defined as the period, Additionally, a protractor could be taped to the top of the pendulum stand, with the ruler taped to the protractor. State the given vector. My partners and I do believe though that we should've done more than three trials in order to get more precise and accurate data. 2 14.73 5 2.94 14.50 0.20 5 Then a spring was hung from the sensor and it was torn to a zero point. This was calculated using the mean of the values of g from the last column and the corresponding standard deviation. The period for one oscillation, based on our value of \(L\) and the accepted value for \(g\), is expected to be \(T=2.0\text{s}\). is measured with the addition of each mass. The conservation of momentum is why the mass will continue to travel up and down through a series of oscillations. each individual of the group. Then a motion sensor was setup to capture the movement of the mass as it traveled through its oscillations. and then released, it will oscillate about the equilibrium position. It was concluded that the mass of the pendulum hardly has any effect on the period of the pendulum but the length on the other hand had a significant effect on the . The displacement, , was taken down each time and the force recorded by data studio was also recorded. 10 0 obj The data correlate close to Hooke's Law, but not quite. 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. follows: For example the group at lab The period, \(T\), of a pendulum of length \(L\) undergoing simple harmonic motion is given by: \[\begin{aligned} T=2\pi \sqrt {\frac{L}{g}}\end{aligned}\]. The baseball is released. The period that you solved for will be your theoretical period. When a box of unknown mass is placed into the trunk of a car, both rear If the mass of the component is 10g, what must the value Don't use plagiarized sources. All of our measured values were systematically lower than expected, as our measured periods were all systematically higher than the \(2.0\text{s}\) that we expected from our prediction. What quantities will you plot in order to determine. The reason why has a negative value is to show that the force exerted by the spring is in the opposite direction of . FOR STUDENTS : ALL THE INGREDIENTS OF A GOOD ESSAY. difference was observed in the experiment. Conclusion From our experiment, I conclude that the period of a pendulum depends on length primarily and agrees with the theory that says for a simple pendulum, . We thus expect to measure one oscillation with an uncertainty of \(0.025\text{s}\) (about \(1\)% relative uncertainty on the period). Data studio and a force sensor, and a position sensor will be used to get accurate measurements of these values. Using a \(100\text{g}\) mass and \(1.0\text{m}\) ruler stick, the period of \(20\) oscillations was measured over \(5\) trials. 6: Speed control unit (controls the turning speed of the chart recorder) But this only works for small angles, about 5 or so. As an example, consider the spring-mass system. I need help with understanding the purpose of this lab. Effects the spring constant and the mass of the oscillator have on the characteristics of the motion of the mass. We suspect that by using \(20\) oscillations, the pendulum slowed down due to friction, and this resulted in a deviation from simple harmonic motion. The motion of a simple pendulum is one of the phenomena that can be used to approximate the simple harmonic motion. At t = 0, the particle is at point P (moving towards the right . This cookie is set by GDPR Cookie Consent plugin. body's average velocity. to the minimum displacement is known as the spring force. In this first part of this lab, you will have a sliding mass on a frictionless air track attached to two springs on one side, and attached to a hanging mass by a string and pulley on the other. Investigate OReilly Automotive, Inc. as an employer, Discuss the Impact of Aesthetics in Surgical Endodontics, Green Chemistrys Potential: Industry and Academia Involvement, Exploring NZ Chinese Identity & Pakeha Ethnicity: Examining White Privilege in NZ, Theatre, Environmental Change, and Lac / Athabasca. SHM means that position changes with a sinusoidal dependence on time. A large value for as shown in Figure 2, Newton's Second Law tells us that the magnitude Simple Harmonic Motion Lab Report Conclusion Eagle Specialty Products Inc. This website uses cookies to improve your experience while you navigate through the website. This sensor was set to a frequency of. Therefore, if we know the mass of a body at equilibrium, we can determine Average 0.20 5 21.20 17.76 0.173 19.19 13.53 0.34 Figure 1: This image shows a spring-mass system oscillating through one cycle about a central equilibrium position. One cycle of kinematics, including . A simple pendulum, is defined as an object with a small mass suspended from a light wire or thread, also known as, the pendulum bob. If we assume the two rear Analytical cookies are used to understand how visitors interact with the website. V= length (m) / time (s) This can be seen in our data because as the value of the mass increases, the F decreases. This cookie is set by GDPR Cookie Consent plugin. In the first part of this lab, you will determine the period, T, of the spring by . Day 3: What is a Battery / How Bright Are You. D- Pend casing extra damping After graphing forces versus displacement, a value of 3.53 N/m was determined as the spring constant. In Objective 1, you may wish to specifically ask the students to 9: Small weights Keeping the paper taut Introduction We first need to understand how to calculate the force of a spring before performing this lab. Whatever you put into the conclusion must be something, which the data you measured will prove or support. is 0.020m. Our complete data is shown in Table 1.0 on the next page. Generally speaking, springs with large Subject-Physices-Professor V. Hooke's Law and Simple Harmonic Motion Lab Report Introduction: This lab is set up for us to to be able to determine the spring constant with two different methods and the gravitational acceleration with a pendulum. We are using the do-it-yourself , simple pendulum as the materials to determine the value of gravitational acceleration and, investigate the relationship between lengths of pendulum to the period of motion in simple, harmonic motion. We transcribed the measurements from the cell-phone into a Jupyter Notebook. = ln A0 / A1 3 0.20 5 21.30 17.73 0.18 19.05 13.57 0.33 Once that was done, we measured an amplitudeof 3cm from the starting point using a ruler. ~ 5";a_x ~10). Why? Mass on a Spring. When a mass is added to the spring it takes the length of, . Physics 1051 Laboratory #1 Simple Harmonic Motion Summary and Conclusions Lab Report 9: Write the expressions for #(,), 6(,), and ;(,) for the oscillator with values of -, 2, and 3 as appropriate. The spring constant is an indication of the spring's stiffness. The value of mass, and the the spring constant. For our particular study we set up a force sensor which would measure a pulling force in the earthward direction. For example, radiation . and then Add to Home Screen. Calculation and Result: For a small angle ( < 10) the period of a simple pendulum is given by 7-25,-(Eq. Lab Report 12: Simple Harmonic Motion, Mass on a Spring. For this lab, we defined simple harmonic motion as a periodic motion produced by a force that follows the following equation: F= - kx. The law is named after 17th-century . record in order to take data for a Hooke's Law experiment when the spring-mass 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. Simple Harmonic Motion Lab Report. The force that causes the motion is always directed toward the equilibrium . 1. Holes open fully Holes open partially stretched or compressed a small distance from its equilibrium position, The mass, string and stand were attached together with knots. This was shown clearly in our data. If you use part of this page in your own work, you need to provide a citation, as follows: Essay Sauce, Simple Harmonic Motion lab report. x}xT{y%3yN2 s2'LB$ 9yL $(E\hjo1hVk[qV#2s>^o~Nck X? Does Hooke's Law apply to an oscillating spring-mass system? Dont know where to start? Figure 5.38 (a) The plastic ruler has been released, and the restoring force is returning the ruler to its equilibrium position. In order to conduct the experiment properly, must you consider the position The restoring force in this system is given by the component of the weight mg along the path of the bob's motion, F = -mg sin and directed toward the equilibrium. 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. This experiment was designed with an intention of gaining a deeper understanding. In Simple harmonic motion, the mean position is a stable equilibrium. In these equations, x is the displacement of the spring (or the pendulum, or whatever it is that's in simple harmonic motion), A is the amplitude, omega is the angular frequency, t is the time, g . for 14-16. download the Lab Report Template Simple Harmonic Motion: Mass On Spring The major purpose of this lab was to analyze the motion of a mass on a spring when it oscillates, as a result of an exerted potential energy. }V7 [v}KZ . @%?iYucFD9lUsB /c 5X ~.(S^lNC D2.lW/0%/{V^8?=} y2s7 ~P ;E0B[f! This cookie is set by GDPR Cookie Consent plugin. We also agreed that we should used a variety of masses rather than increasing each trial's mass by 0.1 g. Melanie Burns WHS Physics Level 1 Kess 2016-17, Lab 02: Acceleration and Instantaneous Speed on an Incline, Lab 1: Effect of Constant Applied Force on Graphs of Motion, Lab 2: Effect of Inertia on Graphs of Motion, Lab 3: Effect of Inertia on Acceleration (More Data Points), Standing on Two Force Plates (Sum of Two Normal Forces), Lab 1: PE, KE and ET for a Cart on an Incline, Unit 5: Periodic and Simple Harmonic Motion and Waves, Lab 4: Further Investigation of Mass/Spring Systems, Day 8: Explaining the Two-Image Photo From Space, Day 01: There is no such thing as electricity. ( 2 ) x = Xmax cos ( t ) The following are the equations for velocity and acceleration. This motion is periodic, meaning the displacement, Abstract. The length of the arc represents the linear, deviation from equilibrium. F_s = -kx F s = kx. Also it was proved to be accurate that the relationship between the period, mass, and the spring constant were in fact, . At the conclusion of the experiment, we discovered that when an object is subjected to a force proportional to its displacement from an equilibrium position, simple harmonic motion results. Write the kinetic, potential and total energy of a baseball having a mass of 0.145kg held 10 meters. determined? 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. We found that the pendulum goes slower than simple pendulum theory at larger angles. >> should print-out the Questions section and answer them individually. In this lab, we will observe simple harmonic motion by studying masses on springs. No- 3. Answer (1 of 5): The sources of errors in a simple pendulum experiment are the following: 1. human errors comes in when measuring the period using a stopwatch. 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. 27: Guidelines for lab related activities, Book: Introductory Physics - Building Models to Describe Our World (Martin et al. period of 0.50s. How will you decrease the uncertainty in the period measurement? In simple harmonic motion, the acceleration of the system, and therefore the net force, is proportional to the displacement and acts in the opposite direction of the displacement. We also worry that we were not able to accurately measure the angle from which the pendulum was released, as we did not use a protractor. 2). Our final measured value of \(g\) is \((7.65\pm 0.378)\text{m/s}^{2}\). Copyright 2023 StudeerSnel B.V., Keizersgracht 424, 1016 GC Amsterdam, KVK: 56829787, BTW: NL852321363B01, Business Law: Text and Cases (Kenneth W. Clarkson; Roger LeRoy Miller; Frank B. What is the uncertainty in the mass measurements? For small angle, we can write the equation of motion of the bob as L x a g sin g (1) In a simple harmonic motion, acceleration is . . Based on this data, does a rubber band A good example of SHM is an object with mass m attached to a spring on a frictionless surface, as shown in Figure 15.2.2. PHY 300 Lab 1 Fall 2010 Lab 1: damped, driven harmonic oscillator 1 Introduction The purpose of this experiment is to study the resonant properties of a driven, damped harmonic oscillator. When a mass, What mass values will you use for this experiment? Let the mean position of the particle be O. Based on the postcode entered, the Find Your Food web serve searches the restaurant master file and, Physics Lab; Mr. Shields Hooke's Law & Springs - PhET Simulation Open the simulation:https://phet.colorado.edu/sims/html/masses-and-springs/latest/masses-and-springs_en.html There are four, Write the kinetic, potential and total energy of a baseball having a mass of 0.145kg held at rest 10 meters above the ground. Advertisement cookies are used to provide visitors with relevant ads and marketing campaigns. the system is balanced and stable. This page titled 27.8: Sample lab report (Measuring g using a pendulum) is shared under a CC BY-SA license and was authored, remixed, and/or curated by Howard Martin revised by Alan Ng. V. Conclusion This experiment for the observation of simple harmonic motion in a simple pendulum determined the different factors that affect the period of oscillation. A pendulum exhibits simple harmonic motion (SHM), which allowed us to measure the gravitational constant by measuring the period of the pendulum. Simple harmonic motion is the motion of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's Law. This involved studying the movement of the mass while examining the spring properties during the motion. %PDF-1.7 The relative uncertainty on our measured value of \(g\) is \(4.9\)% and the relative difference with the accepted value of \(9.8\text{m/s}^{2}\) is \(22\)%, well above our relative uncertainty. For a spring-mass system, such as a block attached to a spring, the spring force is responsible for the oscillation (see Figure 1).