### Mechanics

Schematic of suspension method

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Schematic of vibration measurement

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Curve of resonant frequency

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## LEMI-13 Young's Modulus Apparatus - Resonance Method

Note: oscilloscope not included

Features

• Acquire resonant signal on oscilloscope

• Supporting and suspending methods

• High sensitivity and accuracy

• Affordable

Introduction

When rigid materials are subject to particular stress or forces, deformation (compressed, twisted, stretched, etc) may occur. For many materials, when suffered from force or stress, the resisting or restoring force that tends to return the material to its original shape is proportional to the deformation. Young's Modulus, E, is a constant that describes the material's mechanical property of stiffness and is expressed as the ratio of stress to strain for a material experiencing tensile or compressive stress. This apparatus is designed to study the deformation characteristics of a metal round bar sample by using the dynamic vibrational resonance method.

The dynamic resonance method is to study the vibrational law of a sample. Mathematically, the vibrational law can be described by a four-order partial differential equation, which shows the relationship between the Young's modulus and vibration frequency of a sample and can be related to three parameters of the sample, i.e. the diameter, length, and mass of the sample. While the three parameters are acquired, the Young's modulus can be determined by measuring the vibration resonant frequency of the sample. Two methods, i.e. supporting method and suspending method, are used to determine the resonant frequencies of three samples.

Main Specifications

 Description Specifications Vibration excitation voltage Range: 0 ~ 5 V Receiving transducer voltage Range: 0 ~ 2 V Signal source output power 600 mW Frequency Range: 200 ~ 800 Hz; accuracy: 0.1 Hz Samples Copper, steel and aluminum bars

Parts List

 Description Qty Test platform unit 1 Electric control unit 1 Aluminum, steel and copper bars 1 each Wire and cable 4 Manual 1

Schematic of suspension method

(Click figure to enlarge)

Schematic of vibration measurement

(Click figure to enlarge)

Curve of resonant frequency

(Click graph to enlarge)