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Chapter 13: Problem 12

Explain why the frequency of a damped system is lower than that of the equivalent undamped system.

Short Answer

Expert verified
The frequency of a damped system is lower than that of the equivalent undamped system because the damping force in the system opposes the motion, causing the system to lose energy, which results in a reduction of the system's frequency.

Step by step solution

01

Understanding Undamped system

An undamped system is one where the system is free to vibrate without any external force dampening the vibrations. The frequency of such a system depends entirely on system's natural frequency.
02

Understanding Damped system

A damped system includes an external force that opposes the motion, causing the system to lose energy over time. This external force is referred to as the damping force. In such cases, oscillation amplitude decreases gradually, causing lowered frequency.
03

Comparing Undamped and Damped system

A comparison between these two systems shows that the introduction of damping force in a damped system opposes the system's motion, causing the system to lose energy and subsequently lowering the system frequency. This is why a damped system has a lower frequency than an equivalent undamped system.

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Most popular questions from this chapter

A 200 -g mass is attached to a spring of constant \(k=5.6 \mathrm{N} / \mathrm{m}\) and set into oscillation with amplitude \(A=25 \mathrm{cm} .\) Determine (a) the frequency in hertz, (b) the period, (c) the maximum velocity, and (d) the maximum force in the spring.

Two balls with the same unknown mass \(m\) are mounted on opposite ends of a 1.5 -m-long rod of mass \(850 \mathrm{g}\). The system is suspended from a wire attached to the center of the rod and set into torsional oscillations. If the wire has torsional constant \(0.63 \mathrm{N} \cdot \mathrm{m} / \mathrm{rad}\) and the period of the oscillations is \(5.6 \mathrm{s},\) what's the unknown mass \(m ?\)

The human eye and muscles that hold it can be modeled as a mass-spring system with typical values \(m=7.5 \mathrm{g}\) and \(k=2.5 \mathrm{kN} / \mathrm{m} .\) What's the resonant frequency of this system? Shaking your head at this frequency blurs vision, as the eyeball undergoes resonant oscillations.

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Show that the potential energy of a simple pendulum is proportional to the square of the angular displacement in the small-amplitude limit.
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