Lab Activity 4

Shubha Tewari

4 Lab Activity 4

This lab activity can be done either in person with equipment (the in-person version), or remotely with the linked videos.

Please note: For the videos, do not start making measurements at time zero, as this is arbitrary.

Part 1: Mass-Spring System

In Person Version:

Mass Spring Experiment

Equipment: Vertical suspended spring, set of masses (50g, 100g, 150g), meter sticks, tape, stands. (Use set of hooked masses)

Place one mass on the mass holder attached to the vertical spring. Allow it to come to rest. Mark the equilibrium location of the mass. Enter the value in the first three rows of column 1 in the table in your report – an example blank table is shown below.
Now displace the spring downwards a measured distance from the equilibrium point. This is the amplitude, record it in the table in your report. Be ready with a timing device (you can use your phone). Release the mass and measure the time for 10 complete oscillations. Enter this in the table in your report, in row 1.
Repeat for 3 distinct amplitudes in all, record them in the 2nd column, rows 1 – 3.
Add a second mass, lower it gently and find the new equilibrium point. Repeat the measurement for the same three amplitudes, record in the table in rows 4 – 6.
Do the same for a third mass. Record all your results in the table in your report. Calculate the time period for each, and record this below and in the online google sheet.
In rows 10 – 12 of your table, enter the values for the 3 different masses at 1 amplitude (this is using your data recorded in rows 1, 4, 7 or 2, 5, 8 or 3, 6, 9).

In Person Exercise 1

For a fixed mass, does the measured period of oscillation change in a systematic way (in one direction – either increasing or decreasing) with the amplitude of motion? Compare your data for rows 1 – 3, and separately for rows 4 – 6 and 7 – 9.

Transfer to whole class Google Sheet

Transfer the data for mass, amplitude and time period from your data table to the Google sheet. Each team has three rows. Enter the data from rows 1 – 3 in your table in one set of columns marked “Experiment 1”, the data from rows 4 – 6 under the next set of columns marked “Experiment 2”, and so on. The columns adjacent to your data will automatically use spreadsheet functions AVERAGE and STDEV (standard deviation) to find the average of your 3 time period measurements for a fixed mass, and the % deviation = 100*STDEV/AVERAGE. (Do not overwrite the formulas in these cells!) Enter the results from rows 10 – 12 under Experiment 4.

Now look at your results for the average and % deviation from each experiment and answer the following questions:

In Person Exercise 2

In the context of the results for experiments 1 – 3, review your answer to question 1: does the time period for a fixed mass change systematically with amplitude?

In Person Exercise 3

Does the time period for a fixed amplitude change in a systematic way with mass? Look at the average and % deviation for Experiment 4, and compare this % deviation with that seen in the previous 3 experiments.

In Person Exercise 4

Draw conclusions: Of mass and amplitude, which are the physical quantities that affect the period of the mass-spring system? Is this answer different from what the pendulum group found?

BONUS Exercise

Use your data combined with all the data from other groups on the google sheet to predict a functional relationship between time period and mass.

In Person Table

#	Mass (g)	Amplitude (cm)	Time for 10 cycles	Time period
1
2
3
4
5
6
7
8
9
10
11
12

Remote Version Experiment 1: Find the effect of mass on the time period of oscillation

Remote Experiment 1

Pick the movies labeled X00g_Spring1_AmpA.mp4 where X varies from 1 to 5, corresponding to five different masses suspended from the same spring.
Use the clock indicated at the top of the screen to record the start time and end time for one complete cycle.
You can pause the video and advance it forward or backward frame by frame using the “.” and “,” keys.
Enter these in the table in your report – the table header row is shown below – and use the difference to find the time period for each mass. Also record the amplitude in your table (a rough estimate is good enough).

Remote Experiment 1 exercise

Looking at your experimental data for a given spring for different masses, does the measured period of oscillation change in a systematic way (in one direction – either increasing or decreasing) with the mass?

Remote Experiment 11: Find the effect of Amplitude on time period oscillation

Renote Experiment 2

Pick the movies labeled 200g_Spring1_AmpX.mp4, where X varies from A to D, corresponding to four different oscillation amplitudes for a mass of 200g suspended from Spring 1.
Use the clock indicated at the top of the screen to record the start time and end time for one complete cycle.
You can pause the video and advance it forward or backward frame by frame using the “.” and “,” keys.
Enter these in the table in your report – the table header row is shown below – and use the difference to find the time period for each amplitude. Also record the amplitude in your table (rough estimate).

Remote Experiment 2 exercise

Looking at your experimental data for a fixed mass, does the measured period of oscillation change in a systematic way (in one direction – either increasing or decreasing) with the amplitude of motion?

Remote Experiment 111: Find the effect of the spring on the time period of oscillation

Remote Experiment 3 needs to be changed with videos used: 500g mass with 6 different springs, two amplitudes each, maybe have them choose 3 springs?

Pick the movies labeled 500g_SpringX_AmpA and 500g_SpringX_AmpB, where X varies from 1 to 6, corresponding to 12 oscillations of a 500 gram mass. There are 6 springs, and each has two amplitudes A and B.
Use the clock indicated at the top of the screen to record the start time and end time for one complete cycle for each.
You can pause the video and advance it forward or backward frame by frame using the “.” and “,” keys.
Enter these in the table in your report – the table header row is shown below – and use the difference to find the time period for each mass. Also record the amplitude in your table (a rough estimate is good enough).

Remote Experiment 3 exercise

Looking at your experimental data for a fixed mass, does the measured period of oscillation change in a systematic way (i.e. either increases or decreases) as you move the mass from spring 1 to spring 6?

Remote Experiment 1v: Plot the position of an oscillating mass as a function of time

Remote experiment 4

Pick any one movie.
Note the mass, amplitude, spring number (1 or 2).
Draw a graph of the position of the mass as a function of time on the graph paper provided in the lab document.
Make sure to mark the origin, and number and label the axes.
You can pause the video and advance it forward or backward frame by frame using the “.” and “,” keys.

Remote Exercise 2

Draw conclusions: Now look at all the data for the different experiments by different groups on the online spreadsheet. Of mass and amplitude and the type of spring, which are the physical quantities that affect the period of the mass-spring system?

BONUS Exercise

Use all available data on the google sheet to predict a functional relationship (if one exists, based on your answer to Q2) between time period and (i) mass, (ii) amplitude.

Remote Lab Table Header Row:

Spring #

Mass (g)

Amplitude (cm)

Time 1(s)

Time 2(s)

Period (s)

Part 11: Pendulum System

In part I of the lab, you examined the oscillations of a mass suspended from a spring. In this part of the lab, you will investigate the oscillation period of a pendulum: a mass suspended at the end of a string that swings back and forth under gravity, like a playground swing.

In Person Pendulum Experiment

Equipment: Vertical suspended string, set of 3 masses (10g, 20g, 50g), protractor, tape, stands.

Attach one mass to a string and suspend it from a stand or the edge of the table. Allow it to come to rest. Enter the mass in the table in your report, rows 1 – 3. A blank example table is shown below.
Now displace the mass laterally a measured distance from the equilibrium point. This is the amplitude, and can be measured as an angle using the protractor. (Do not make this too large – keep the angles less than 45 degrees.) Be ready with a timing device (you can use your phone). Release the mass and measure the time for 10 complete oscillations. Enter your data in your table, row 1.
Repeat for 3 amplitudes in all, record them in the 2nd column, rows 1 – 3.
Add a second mass and allow it to come to rest. Repeat the measurement in step 2 for the same three distinct amplitudes, record values in rows 4 – 6.
Do the same for a third mass. Calculate and record all your time period results in your table, and in the online google sheet.
Now use 1 mass, and 1 amplitude used in rows 1 – 9, and change the length of the string, and measure the time for 10 swings. Record data in rows 10 – 12.

In Person Pendulum Table

#	Mass (g)	Amplitude(degrees)	Time for 10 cycles	Time period
1
2
3
4
5
6
7
8
9
	Length	Amplitude (degrees)	Time for 10 cycles	Time period
10
11
12

In Person Exercise 1

For a fixed mass, does the measured period of oscillation change in a systematic way (in one direction – either increasing or decreasing) with the amplitude of motion? Compare your data for rows 1 – 3, and separately for rows 4 – 6 and 7 – 9.

Transfer to whole class Google Sheet

Transfer the data for mass, amplitude and time period from your data table to the Google sheet. Each team has three rows. Enter the data from rows 1 – 3 in your table in one set of columns marked “Experiment 1”, the data from rows 4 – 6 under the next set of columns marked “Experiment 2”, and so on. The columns adjacent to your data will automatically use spreadsheet functions AVERAGE and STDEV (standard deviation) to find the average of your 3 time period measurements for a fixed mass, and the % deviation = 100*STDEV/AVERAGE. (Do not overwrite the formulas in these cells!) Enter the results from rows 10 – 12 under Experiment 4.

Now look at your results for the average and % deviation from each experiment and answer the following questions:

In Person Exercise 2

In the context of the results for experiments 1 – 3, review your answer to question 1: does the time period for a fixed mass change systematically with amplitude?

In Person Exercise 3

Does the time period for a fixed amplitude change in a systematic way with mass? In other words, what is the average and standard deviation of all 9 measurements in rows 1 – 9 of your data table? Look at the end of the set of columns for this value.

In Person Exercise 4

Now look at your data for the average and the % deviation for different string lengths for a fixed mass and fixed amplitude (Experiment 4). How does this % deviation compare with that reported in the previous questions? Does the period change with the length of the pendulum?

In Person Exercise 5

Draw conclusions: Of mass, string length, and amplitude, which are the physical quantities that influence the period of the pendulum? Is this answer different from what the mass-spring group found?

Remote Pendulum Experiment

Design your own experiment

to answer the following question: what physical quantities does the period of oscillation depend on? Possible physical parameters you can vary: mass, length of the pendulum, amplitude of the swing.

What you should report here: describe your experiment design, plan the data you need to take to answer this question, construct the relevant data table, and make inferences. Include a picture of your experimental setup.

Remote Pendulum Exercise

Draw conclusions: Of mass, string length, and amplitude, which are the physical quantities that influence the period of the pendulum? Is this answer different from the relevant physical quantities for the mass-spring system?