System Dynamics
System Dynamics
3rd Edition
ISBN: 9780073398068
Author: III William J. Palm
Publisher: MCG
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Chapter 4, Problem 4.1P
To determine

The translational spring constant of helical coil spring.

Expert Solution & Answer
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Answer to Problem 4.1P

The translational spring constant of helical coil spring is 2894lb/ft.

Explanation of Solution

Given information:

The number of turn in a coil is 6, the diameter of the coil is 4in, the diameter of the wire is 0.5in, the shear modulus of the material is 1.7×109lb/ft2.

Write the expression for the translational spring constant.

k=Gd464nR3 (1)

Here, the translational spring constant is k, the shear modulus of the material is G, the radius of the coil is R, the diameter of the wire is d and the number of turn in a coil is n.

Write the expression for radius of the coil.

R=D2 (2)

Here, the radius of the spring is R, the diameter of the spring is D.

Calculation:

Substitute 4in for D, Equation (2).

R=4in2=(4in)(1ft12in)2=16ft

Substitute 16ft for R, 1.7×109lb/ft2 for G, 6 for n and 0.5in for d in Equation (1).

k=1.7×109lb/ft2(0.5in)464×6×(16ft)3=1.7×109lb/ft2((0.5in)(1ft12in))464×6×(16ft)3=1.7×109lb/ft2(3.014×106ft4)1.77ft32894lb/ft.

Conclusion:

The translational spring constant of helical coil spring is 2894lb/ft.

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Chapter 4 Solutions

System Dynamics

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