Physics 1202 - SHM- worksheets - Winter 2023 - Rishan

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Simple Harmonic Motion - 5 — Data and Work Sheets Simple Harmonic Motion - Physics 1202B 2022-2023 Please circle the appropriate values Course 1102B 1202B 1402B 1502B Lab Section 002 003 004 005 006 007 008 009 010 013 014 Lab Subsection A B C D Name First: Rishan Last: Rajakulathilakan Student # 2 5 1 3 1 4 5 5 5 Lab Partner First:Yanishka Last:Gahlot Lab Station # 1 Date 2023 – 01 - 31 Demonstrator Rina and Baria Disclaimer: Please note that some but not all questions in this lab writeup will be graded. EXPERIMENT 1: MEASURING THE SPRING CONSTANT OF THE SPRING APPARATUS: steel helical spring, masses, meter ruler and mirror (to eliminate parallax) METHOD You should have a setup as shown in Figure 1. The spring is hung on a force sensor. The force sensor and the ultrasonic device are not used in Experiment 1 when the spring constant is measured, but will be used in Experiment 2. Record in Table 1 the position of the lower end of the helical spring with no masses attached. This is the equilibrium position, x 0 , of the spring. Now, add a mass to the spring and record the mass ( m ) attached to the spring, and the position ( x ) of the lower end of the spring, in Table 1. (Note that you should always start with the lowest mass so as to not elongate the spring past its breaking point. The displacement ( x x 0 ) should be at least 3 cm and no more than 20 cm . Continue to increase the load on the spring by small increments, by either adding masses or by substituting a heavier mass, and record the position of the lower end of the spring for each mass. Add masses gently so that the spring extends monotonically, i.e., without bouncing the load on the spring. Repeat this process for at least 4 different masses.

Simple Harmonic Motion - 6 − − Figure 1: Setup of vertical mass-spring system. The spring is suspended vertically and extended due to the weight of a mass attached to the end. The mirror is used to reduce measurement errors due to parallax. The force and motion sensors are not shown in this schematic. Calculate the corresponding displacement ( x x 0 ) of the spring for each mass, and record ( x x 0 ) in Table 1. The displacement is the increase in length from the equilibrium position of the spring. Include an estimate of uncertainty in the column heading for each variable. Table 1: Static (non-oscillatory) force-displacement data for determining the spring constant of the mass-spring system Mass m (g) ±0.1g Position x (cm) ±0.5cm Weight (N) (mass x gravity) ±0.1N Displacement ( x - x 0 ) (m) ±0.5 0.0 42.0 cm 0.0 0.0m 50g 42.0cm 490.0N 0.0m 100.0g 44.9cm 980.0N 2.9m 200.0g 55.5cm 1960.0N 13.5m

Simple Harmonic Motion - 7 EXPERIMENT 1(a): DETERMINATION OF THE SPRING CONSTANT 1. Using Excel , plot weight (in Newtons) versus displacement ( x − x 0 ). 2. Fit a straight line without forcing the fitted line through the origin to determine the spring constant k . In Excel , use the “Add Trendline” function to add a linear line with the display equation option selected. 3. Determine the slope. – we know that the slope is equal to the spring constant What is the spring constant? - 30.127 N/m EXPERIMENT 2: DETERMINATION OF THE PARAMETERS OF A SIMPLE HARMONIC MOTION In this experiment, you will record the position, velocity, acceleration and force using the ultrasonic position-measurement device and a force sensor. The parameters of the oscillation will be obtained by graphical analysis of data collected by the Logger Pro software on the lab computers. Each group will measure the oscillation of the vertical mass-spring system using the same spring but with two different masses but the same amplitude. Then they change the am- plitude and repeat the experiment for the two different masses chosen. The students will analyze the data each time to investigate the effects of changing the mass as well as changing the amplitude on the motion of the simple harmonic oscillator. EXPERIMENT 2(a): SETUP In this experiment, you will now use the Vernier force and position sensors to acquire data from the oscillation of a mass on a spring, as shown in Figure 2. 1. Ensure that both sensors are connected to the mini Lab Quest data hub, and the hub is con- nected to the computer. 2. Position the ultrasonic sensor directly underneath the spring. There needs to be a minimum of 15 cm between the sensor and the mass on the spring for the sensor to record accurately. 3. Select 10 N range for the force sensor. 4. Select “cart” position for the ultrasonic position sensor.

Simple Harmonic Motion - 8 We want to choose a mass such that oscillations will be about an equilibrium position that stretches the spring by approximately 8-12 cm. 1. Start up the Logger Pro software, and select the use of both the force and the position sensors. 2. Hang your chosen mass, and let the spring-mass system come to an equilibrium. You may have to wait a minute or so for it to come to rest. 3. Under the menu “Experiment”, choose “zero” to zero both the force and the position sensors (see Figure 3). 4. To start collecting data, click on the green arrow button labelled “Collect”. 5. The Logger Pro is setup to collect 25 measurements per second over a period of 10 seconds. 6. Without any motion, collect a baseline set of data (see Figure 4). 7. The vertical axis range of each graph can be changed. You may click on any number on the vertical axis to change the range. EXPERIMENT 2(b): WHAT TO MEASURE 1. Each station will accommodate two students who work in pairs using the same spring. You will use two different masses, allowing the spring to stretch by approximately 8-12 cm from the equilibrium each time. 2. You will then setup and record two sets of oscillations using two different amplitudes (e.g., amplitudes between 1-3 cm for the first set and 3-6 cm for the other set). Label and save your data. You will need to use the data for the two sets of amplitudes later in the analysis section. 3. While working together, lab partners will need to take turns using the equipment. Once you finished acquiring data for one mass and one amplitude, save your work on the Desktop, and open it with Excel to do the analysis (see the Analysis sections). Be sure to give your file a meaningful name when saving your work so you know which mass and amplitude you used. Then acquire data for the same mass using a different amplitude. Analyze the data and save your work under a different name. Repeat the above procedure for a different mass and the above two amplitudes. You should acquire 4 sets of data (i.e., two different masses, two different amplitudes).

Simple Harmonic Motion - 9 Figure 2: Setup for Experiment 2. The spring is suspended vertically and extended due to the weight of a mass attached to the end. This resting position is the equilibrium position, and the mass will oscillate about this point during simple harmonic motion.

Simple Harmonic Motion - 10 Figure 3: After the chosen mass is hung on the spring and the system comes to an equilibrium position, zero the force and the position sensors, as shown above.

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