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Chapter 13: Problem 4

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 the horizontal and vertical mass-spring systems will not change because their frequencies don't depend on gravity. The frequency of the simple pendulum will decrease due to the decreased gravitational acceleration on the Moon.

Step by step solution

01

Determine the frequency change in horizontal mass-spring system

The natural frequency of an ideal horizontal mass-spring system is given by \(f = \frac{1}{2\pi} \sqrt{\frac{k}{m}}\), where \(k\) is the spring constant and \(m\) is the mass. Since neither \(k\) nor \(m\) are affected by the change in location to moon, the frequency of a horizontal mass-spring system will not change.
02

Determine the frequency change in vertical mass-spring system

Just like in the horizontal system, the change in gravity doesn't impact the spring constant \(k\) or mass \(m\) in a vertical mass-spring system. Hence the frequency of the vertical mass-spring system would also not change on the moon.
03

Determine the frequency change in a 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. The frequency of the pendulum is inversely proportional to the square root of acceleration due to gravity. As gravity on the moon is about one sixth of what is on earth, the frequency will decrease, resulting in the pendulum swinging more slowly on the moon.

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Most popular questions from this chapter

A \(600-\mathrm{g}\) block on a frictionless, horizontal surface is attached to a rather limp spring with \(k=8.7 \mathrm{~N} / \mathrm{m}\). A second block rests on the first, and the whole system executes simple harmonic motion with period \(2.1 \mathrm{~s}\). When the amplitude of the motion is increased to \(35 \mathrm{~cm}\), the upper block just begins to slip. What's the coefficient of static friction between the blocks?

A wheel rotates at \(720 \mathrm{rpm}\). Viewed from the edge, a point on the wheel appears to undergo simple harmonic motion. What are (a) the frequency in \(\mathrm{Hz}\) and (b) the angular frequency for this SHM?

A mass-spring system with spring constant \(k=63.7 \mathrm{~N} / \mathrm{m}\) is oscillating with angular frequency \(2.38 \mathrm{~s}^{-1}\) and total energy \(7.69 \mathrm{~J}\). Find (a) its amplitude and (b) its maximum speed.

A particle of mass \(m\) has potential energy given by \(U=a x^{2}\), where \(a\) is a constant and \(x\) is the particle's position. Find an expression for the frequency of simple harmonic oscillations this particle undergoes.

A doctor counts 75 heartbeats in \(1.0\) minute. What are the corresponding period and frequency?
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