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Chapter 13: Problem 6

How would the frequency of a horizontal mass-spring system change if it were taken to the Moon? Of a vertical mass-spring system? Of a simple pendulum?

Short Answer

Expert verified
The frequency of a horizontal or vertical mass-spring system would not change if moved to the Moon because they are not influenced by gravity. The frequency of a simple pendulum would however decrease if taken to the Moon due to the lower gravitational acceleration.

Step by step solution

01

Analyzing effects on the Horizontal Mass-Spring system

In a horizontal mass-spring system, gravity has no impact on the motion of the spring. This means that regardless of where you place it - whether that is on Earth or on the Moon - the frequency would remain unchanged, because the frequency formula \(f = \frac{1}{2\pi}\sqrt{\frac{k}{m}}\) doesn't contain 'g' (gravitational acceleration).
02

Analyzing effects on the Vertical Mass-Spring system

OUnlike the horizontal mass-spring system, the frequency of the vertical mass-spring system is affected by gravity, via the spring's weight. However, when the system reaches an equilibrium position, the weight is absorbed by the spring force, and the oscillation still depends only on the mass of the object and the spring constant. Therefore, the frequency of a vertical mass-spring system also wouldn't change if it were moved to the Moon.
03

Analyzing effects on the Simple Pendulum system

Because the frequency of a simple pendulum is affected by gravity, the frequency would change if it were taken to the Moon. The formula for the frequency of a pendulum is \(f = \frac{1}{2\pi}\sqrt{\frac{g}{l}}\) where 'g' is the acceleration due to gravity and 'l' is the length of the pendulum. As the gravity on the moon is about one-sixth of that on Earth, the frequency will be smaller when the pendulum is on the Moon.

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Most popular questions from this chapter

A \(342-\mathrm{g}\) mass is attached to a spring and undergoes simple harmonic motion. Its maximum acceleration is \(18.6 \mathrm{m} / \mathrm{s}^{2}\) and its maximum speed is \(1.75 \mathrm{m} / \mathrm{s}\). Determine (a) the angular frequency, (b) the amplitude, and (c) the spring constant.

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.

One pendulum consists of a solid rod of mass \(m\) and length \(L\) and another consists of a compact ball of the same mass \(m\) on the end of a mass less string of the same length \(L\). Which has the greater period? Why?

A doctor counts 68 heartbeats in 1.0 minute. What are the corresponding period and frequency?

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.
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