[:PiraScheme#Mechanics: Table of Mechanics Demonstration] [:MEEquipmentList: List of Mechanics Equipment & Supplies] [:Demonstrations:Lecture Demonstrations]

# Driven Mass on a Spring, 3A60.39

Topic and Concept:

• Oscillations, [:Oscillations#DrivenRes: 3A60. Driven Mechanical Resonance]

Location:

attachment:DrivenMassSpring18-400.jpg

Abstract:

A function generator drives a spring with a suspended mass. The frequency is adjusted until resonance is reached.

 Equipment Location ID Number Function Generator [:MechanicsCabinetBayB1: ME, Bay B1, Shelf #2] Pasco Driver [:MechanicsCabinetBayB1: ME, Bay B1, Shelf #2] BNC Wire [:MechanicsCabinetBayA5: ME, Bay A5, Shelf #2] Springs [:MechanicsCabinetBayA5: ME, Bay A5, Shelf #2] Mass [:MechanicsCabinetBayA5: ME, Bay A5, Shelf #2] Rod and Clamps Rod and tackle cabinet located near main lecture halls.

Important Setup Notes:

• Demonstration may require practice.

Setup and Procedure:

1. Vertically mount 3/4" rod to lecture bench using blue table clamp.
2. Horizontally mount 1/4" rod to the vertical rod using a right angle clamp.
3. Mount the Pasco driver to the 1/4" rod so that the driving component will move in a vertical direction.
4. Place the function generator on the table near the rod, and plug it in.
5. Connect the driver to the function generator with the two wires. Positive to positive. Ground to ground.
6. Hang the spring from the driver.
7. Hang the mass from the spring.
8. When ready, turn on the function generator by pressing the "On" button.
9. The mass will begin to oscillate in a vertical direction. Adjust the frequency of oscillation by changing the driving frequency set on the function generator so that the system approaches resonance (some practice beforehand is recommended).

Cautions, Warnings, or Safety Concerns:

• N/A

Discussion:

The dynamics of this system are described by a linear, inhomogeneous, second order, 2D (one spatial dimension, one time dimension) differential equation (see [http://hyperphysics.phy-astr.gsu.edu/hbase/oscdr.html Wikipedia - Driven Oscillator]). The inhomogeneous part comes from the driving force which is sinusoidal having a general form of

F(t) = F0 * cos(ω*t - φ)

where F0 is the driving amplitude, ω is the driving frequency, and φ is the phase angle. F0 and ω are set on the function generator. The steady-state solution (letting t go to infinite) for no damping (we can assume that for this system) is given by

x(t) = A*

 attachment:DrivenMassSpring13-250.jpg attachment:DrivenMassSpring14-250.jpg attachment:DrivenMassSpring15-250.jpg attachment:DrivenMassSpring16-250.jpg attachment:DrivenMassSpring17-250.jpg attachment:DrivenMassSpring19-250.jpg attachment:DrivenMassSpring20-250.jpg attachment:DrivenMassSpring21-250.jpg attachment:DrivenMassSpring22-250.jpg attachment:DrivenMassSpring23-250.jpg attachment:DrivenMassSpring24-250.jpg attachment:DrivenMassSpring25-250.jpg attachment:DrivenMassSpring26-250.jpg attachment:DrivenMassSpring27-250.jpg attachment:DrivenMassSpring28-250.jpg attachment:DrivenMassSpring29-250.jpg attachment:DrivenMassSpring30-250.jpg

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