Docsity
Log inSign up
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search Store documents

The best documents sold by students who completed their studies

Search through all study resources
Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

University Rankings

Discover the best universities in your country according to Docsity users

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

From our blog

Exams and Study
Go to the blog

Lab 8: Simple Harmonic Motion, Lab Reports of Physics

Berkeley City CollegePhysics

Complete lab report of Simple Harmonic Motion chapter (20/20 score grade)

Typology: Lab Reports

2020/2021

Uploaded on 12/05/2021

AnttiKokko
AnttiKokko 🇺🇸

5

(5)

8 documents

1 / 4

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Hamza Hachim
PHYS 3A
Professor Rosa Alvis
11/9/2021
Lab 8: Simple Harmonic Motion
Objective: To study simple harmonic motion by conducting, measuring, and comparing
experimental and theoretical period values by utilizing a vertical mass-spring system, Hooke's
Law apparatus.
Overview:
We will analyze how the force applied to spring by a mass corresponds to the length of time the
spring is extended. The force exerted by a spring on a mass is defined by Hooke’s law. This
force is proportional to how far the spring is extended from its equilibrium position, and it is
always guided back to the equilibrium position, as described. This equation can be written as:
FA=kΔX, k = FA/Δx
The variable F is the force the spring exerts on the attached mass and ΔX is the distance the
spring is stretched or compressed from equilibrium. The constant k is the spring constant or the
force constant. We will use Hooke’s law equation to find the spring constant of several hanging
masses so we can ultimately determine our theoretical period.
In the case of the vertical spiral spring used in this experiment, when a mass is hooked to the
spring and the system is lowered to its new equilibrium position, the spring stretches until the
restoring force due to the additional stretch of the spring equals the weight of the added mass.
The displacement, x, is the displacement of the system from its position before any mass was
added, i.e. the displacement from the original equilibrium position.
If the mass at the end of the spring is pulled down and released, the system oscillates. For a
system in which the restoring force obeys Hooke’s Law, the oscillatory motion is called simple
harmonic motion. It can be shown that for a body moving in simple harmonic motion, T, the
theoretical period of the motion (the time for one complete oscillation) is given by:
T = 2π , δT = ½ T δk/k
𝑀𝑇
𝐾
We will evaluate and measure how the oscillating period changes with the increase or decrease
of mass. The more massive the object, the longer the period. The mass (m) and the force
constant (k) are the only factors that affect the oscillating period of harmonic motion. Hooke’s
pf3
pf4

Partial preview of the text

Download Lab 8: Simple Harmonic Motion and more Lab Reports Physics in PDF only on Docsity!

Hamza Hachim PHYS 3A Professor Rosa Alvis 11/9/ Lab 8: Simple Harmonic Motion Objective : To study simple harmonic motion by conducting, measuring, and comparing experimental and theoretical period values by utilizing a vertical mass-spring system, Hooke's Law apparatus. Overview: We will analyze how the force applied to spring by a mass corresponds to the length of time the spring is extended. The force exerted by a spring on a mass is defined by Hooke’s law. This force is proportional to how far the spring is extended from its equilibrium position, and it is always guided back to the equilibrium position, as described. This equation can be written as: FA=kΔX, k = FA/Δx The variable F is the force the spring exerts on the attached mass and ΔX is the distance the spring is stretched or compressed from equilibrium. The constant k is the spring constant or the force constant. We will use Hooke’s law equation to find the spring constant of several hanging masses so we can ultimately determine our theoretical period. In the case of the vertical spiral spring used in this experiment, when a mass is hooked to the spring and the system is lowered to its new equilibrium position, the spring stretches until the restoring force due to the additional stretch of the spring equals the weight of the added mass. The displacement, x, is the displacement of the system from its position before any mass was added, i.e. the displacement from the original equilibrium position. If the mass at the end of the spring is pulled down and released, the system oscillates. For a system in which the restoring force obeys Hooke’s Law, the oscillatory motion is called simple harmonic motion. It can be shown that for a body moving in simple harmonic motion, T, the theoretical period of the motion (the time for one complete oscillation) is given by: T = 2π , δT = ½ T δk/k 𝑀𝑇 𝐾 We will evaluate and measure how the oscillating period changes with the increase or decrease of mass. The more massive the object, the longer the period. The mass (m) and the force constant (k) are the only factors that affect the oscillating period of harmonic motion. Hooke’s

law explains that if a mass is attached to a spring and then displaced from its rest position and released, it will oscillate around that position in harmonic motion. This is an important type of periodic oscillation where the acceleration is proportional to the displacement from equilibrium, in the direction of the position. We will measure and compare both the theoretical and experimental periods and evaluate whether they agree with each other by performing a discrepancy test. Procedure Summary :

  1. Gather equipment: spring, masses, meter stick, rod(s), base, clamps, etc.
    1. Experimentally determine the period, Texp by displacing the mass by a few centimeters and let go.
    2. Measure the time for 5 to 10 complete oscillations, TN osc, and its uncertainty, δTN osc
    3. Calculate the period for one oscillation, Texp = TN osc/N, and its uncertainty, δTexp = δTN osc/N
    4. Repeat step 4 two more times displacing the mass with various amplitudes and assessing whether the amplitude of displacement affects the period.
  2. Compute an average experimental period from your three measurements of the period and verify if the average experimental period agrees with our theoretical period. Data: Theoretical Values Table: Hanging mass (kg) Hanging weight (N) Position (m) Δx (m) K (N/m) K 0.05 (^) 0.5 0.696 (^0) x x 0.150 (^) 1.47 0.796 (^) 0.100 14.7 ±0. 0.250 (^) 2.45 0.895 (^) 0.199 12.31 ±0. 0.350 (^) 3.43 0.994 (^) 0.298 11.51 ±0.

%difference = |Tth - Texp|/Tth x100 = |1.100 - 1.100|/1.100 x100 = (0/1.100)x100 = 0% Discrepancy test = |Tth - Texp| ≤ 2(Tth + Texp) = 0 ≤ 2(0.003) = 0 ≤ 0.006 ✓ Sources of error: Two potential errors that could have affected the experiment: First, the random error of an inconsistent reaction to time noting which could result in inconsistent time oscillation values. Second, the environment in which the experiment has taken place could have inconsistent Ventilation or air circulation could alter and disrupt the condition in the room affecting the oscillation of the mass (wind speed not being constant) results in inaccurate readings. To prevent these types of errors, we could measure more cycles for each displacement and modify the environment to have a more constant air temperature and pressure. Conclusion : The calculated theoretical period value was similar to the calculated experimental value proving Hooke’s law. It was demonstrated that mass had an effect and is independent of the period of oscillation against time. Using Hooke’s law, we were able to calculate the proportionality constant, k, for an ideal spring. We also measured the period for a real spring with different weights. Our first set of calculations have proved the extension of a spring is in direct proportion with the load applied to it. Similarly, mass is directly proportional to the period of oscillation. Increasing the mass increases the period of oscillation as indicated by the formula 2π. On the other hand, the amplitude did 𝑀 𝐾 not seem to affect the values of T or the period of simple harmonic motion.