This system is qualitatively similar to one that you may be more familiar with: a mass on a spring. The following table is provided to help your understanding of the system and how it is related to the linear mass and spring system. Spring-Mass System The force F exerted by a spring on a mass m is proportional to the displacement and is given by Hooke's Law for small displacements F = -kx where k is the spring constant. The period T of the spring-mass system is T = 27₁ 'm k Torsion Pendulum The torque 7 exerted by a wire on a disk is proportional to the angular displacement for small angles and is given by T = -KO where is the torsion constant. The period T of the torsion pendulum is given by T= For you to find out! Table 1: A comparison of the spring-mass system with the torsion pendulum.

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How to find T?

This system is qualitatively similar to one that you may be more familiar with: a mass on
a spring. The following table is provided to help your understanding of the system and how
it is related to the linear mass and spring system.
Spring-Mass System
The force F exerted by a spring on a mass
m is proportional to the displacement and is
given by Hooke's Law for small displacements
F: = -kx
where k is the spring constant.
The period T of the spring-mass system is
'm
k
T = 27.
Torsion Pendulum
The torque 7 exerted by a wire on a disk is
proportional to the angular displacement for
small angles and is given by
T = -KO
where is the torsion constant.
The period T of the torsion pendulum is
given by
T= For you to find out!
Table 1: A comparison of the spring-mass system with the torsion pendulum.
Transcribed Image Text:This system is qualitatively similar to one that you may be more familiar with: a mass on a spring. The following table is provided to help your understanding of the system and how it is related to the linear mass and spring system. Spring-Mass System The force F exerted by a spring on a mass m is proportional to the displacement and is given by Hooke's Law for small displacements F: = -kx where k is the spring constant. The period T of the spring-mass system is 'm k T = 27. Torsion Pendulum The torque 7 exerted by a wire on a disk is proportional to the angular displacement for small angles and is given by T = -KO where is the torsion constant. The period T of the torsion pendulum is given by T= For you to find out! Table 1: A comparison of the spring-mass system with the torsion pendulum.
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