MECE 102 Engineering Mechanics Lab A First Year Course in Newtonian Mechanics, Experimentation, and Computer Tools Created by the Faculty of the Mechanical Engineering Department in the Kate Gleason College of Engineering at RIT

Week 9 Lecture Simple Harmonic Motion This week we will study: The transient response of a spring – mass system Use LabVIEW and the Ultrasonic transducer to acquire data The relationships between Gravitational PE of the Mass Kinetic Energy of the Mass Elastic Potential Energy of the Spring

iCLICKER: The week 9 Lab Experiment studies Simple Harmonic Motion. Which one of the following correctly identifies the system being analyzed? Select your Answer: A.Mass B.Spring C.Mass and Spring D.Mass, Spring and Support structure E.None of the above

iCLICKER: The week 9 Lab Experiment studies Simple Harmonic Motion. Which one of the following correctly identifies the system being analyzed? Select your Answer: A.Mass B.Spring C.Mass and Spring D.Mass, Spring and Support structure E.None of the above

FORMULATE: State the Known Information Given the mass, m, of a dead weight suspended from a linear elastic spring. Given the spring constant, K, of the spring, and the initial displacement, z 1, of the mass, m, from the neutral position. Find the transient response of the vertical position, z(t), of the mass, m, as a function of time, t.

FORMULATE: Identify the Desired Information

FORMULATE: Identify Assumptions

Figure 9.1: Schematic Diagram of a mass suspended from a spring with a transducer oriented to measure oscillation. CHART: Schematic Diagram Note the Neutral Position of the spring, with no external mass applied, is different than the Equilibrium Position, z 0, associated with the spring and mass.

Figure 9.1: Schematic Diagram of a mass suspended from a spring with a transducer oriented to measure oscillation (zoomed-in). CHART: Schematic Diagram

CHART: Free Body Diagram Figure 9.2: Free Body Diagrams of a mass and spring, constrained to move in tandem.

CHART: Data Table Each row in the STATE TABLE corresponds to one unique instant of time for the spring – mass system.

CHART: Example Data Plot

iCLICKER: Which of the following statements is FALSE? Select your Answer: A.When the spring-mass system passes through the equilibrium position, the KE of the mass is at its maximum. B.The Mass changes direction at the minimum and maximum peak values of elastic spring PE. C.All of the Energy plots are in phase.

iCLICKER: Which of the following statements is FALSE? Select your Answer: A.When the spring-mass system passes through the equilibrium position, the KE of the mass is at its maximum. B.The Mass changes direction at the minimum and maximum peak values of elastic spring PE. C.All of the Energy plots are in phase.

Period =  EXECUTE: CHART: Example Data Plot Examples of in-phase and out-of-phase data

Example Problem A 200 [gram] mass is suspended from a spring that has a spring constant of 5 [N/m]. The mass is displaced slightly and released to induce vertical motion. Calculate the Period, , of the oscillating spring-mass system [sec].

Example Problem

Can you think of any practical everyday situations where “out of phase” signals are useful?

Noise-cancelling Headphones

Can you think of any practical everyday situations where “out of phase” signals are useful? Noise-cancelling Headphones Earthquake “resistant” structures

Can you think of any practical everyday situations where “out of phase” signals are useful? Noise-cancelling Headphones Earthquake “resistant” structures Spoons! stabilize-parkinsons-tremors/

EXECUTE: Recall the Governing Equations

EXECUTE: Apply and Simplify the Governing Equations

Also recall the initial condition of the mass – spring system: position

EXECUTE: Apply and Simplify the Governing Equations Eqn is not a standard Algebraic equation. What “type” of equation is equation 9.28?

EXECUTE: Apply and Simplify the Governing Equations Eqn is not a standard Algebraic equation. Eqn is known as a non-homogenous linear ordinary differential equation.

EXECUTE: Apply and Simplify the Governing Equations Eqn is not a standard Algebraic equation. Eqn is known as a non-homogenous linear ordinary differential equation. To approximate solution to 9.28: - Analyze raw data from Lab experiment  Studio - Numerical simulation of system  Studio - Analytical Mathematical solution  “Ordinary Diff Eq” course

EXECUTE: Iterate Multiple trials will be conducted in LAB. Each group member will conduct their own, unique trial. Test parameters that should be varied include: 1.Amount of Mass hanging from spring 2.Unique initial displacement values, z 1 3.Conduct at least one trial with z 1 > 0 and at least one trial with z 1 < 0

Week 9 Lab Experiment

Homework Prior to LAB tomorrow Read section 9.2 of the textbook Watch LAB Videos Complete the on-line LAB quiz in myCourses Attempt to solve all assigned Homework problems in your logbook before RECITATION. WEEK 9 Problem Set: From Section 9.5: Problems 2, 3, 4, 7 Lab Report is due Monday by 6pm! The Scribe must upload the LAB REPORT to the myCourses Dropbox.