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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 both the horizontal and vertical mass-spring systems wouldn't change if moved to the Moon, as their frequencies are independent of gravity. Contrastingly, the frequency of a simple pendulum would decrease due to the lower gravitational acceleration on the Moon.

Step by step solution

01

Analyze the horizontal mass-spring system

The frequency of the horizontal mass-spring system is given by \( f = \frac{1}{2\pi}\sqrt{\frac{k}{m}} \). From this formula, it can be seen that the frequency depends on the spring constant (\( k \)) and the mass (\( m \)), but not on gravity. Therefore, the frequency of a horizontal mass-spring system would not change if it were taken to the Moon.
02

Analyze the vertical mass-spring system

Similar to the horizontal case, the frequency of the vertical mass-spring system is also given by \( f = \frac{1}{2\pi}\sqrt{\frac{k}{m}} \). The frequency is independent of the force of gravity. Therefore, taking it to the Moon would not change the frequency.
03

Analyze the simple pendulum

The frequency of a simple pendulum is given by \( f = \frac{1}{2\pi}\sqrt{\frac{g}{l}} \), where \( g \) is the acceleration due to gravity and \( l \) is the length of the pendulum. Upon taking the pendulum to the moon where the gravitational force is about a sixth that on Earth (\( g_{moon} \approx \frac{g_{earth}}{6} \)), the smaller gravity will result in a reduction of the frequency.

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Most popular questions from this chapter

Write expressions for simple harmonic motion (a) with amplitude \(10 \mathrm{cm},\) frequency \(5.0 \mathrm{Hz},\) and maximum displacement at \(t=0\) and (b) with amplitude \(2.5 \mathrm{cm},\) angular frequency \(5.0 \mathrm{s}^{-1},\) and maximum velocity at \(t=0\)

Two mass-spring systems with the same mass are undergoing oscillatory motion with the same amplitudes. System 1 has twice the frequency of system \(2 .\) How do (a) their energies and (b) their maximum accelerations compare?

A particle undergoes simple harmonic motion with amplitude \(25 \mathrm{cm}\) and maximum speed \(4.8 \mathrm{m} / \mathrm{s} .\) Find the (a) angular frequency, (b) period, and (c) maximum acceleration.

Explain how simple harmonic motion might be used to determine the masses of objects in an orbiting spacecraft.

Two balls each of 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 \(m ?\)
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