/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 18 Pendulum A has a bob of mass \(m... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 14: Problem 18

Pendulum A has a bob of mass \(m\) hung from a string of length \(I_{i}\) pendulum \(B\) is identical to \(A\) except its bob has mass \(2 m\). Compare the frequencies of small oscillations of the two pendulums.

Short Answer

Expert verified
Question: Compare the frequencies of small oscillations of two pendulums, A and B, where pendulum A has a bob of mass m and string length L, and pendulum B has a bob of mass 2m and the same string length L as pendulum A. Answer: The frequencies of small oscillations of pendulums A and B are the same.

Step by step solution

01

Recall the formula for the frequency of a simple pendulum

The formula for the frequency of a simple pendulum is given by: $$ f=\frac{1}{2\pi}\sqrt{\frac{g}{L}} $$ where \(f\) is the frequency, \(g\) is the acceleration due to gravity, and \(L\) is the length of the pendulum.
02

Find the frequency of pendulum A

Since pendulum A has a length of \(L_i\) and a bob of mass \(m\), we can substitute these values into the frequency formula to find its frequency: $$ f_A=\frac{1}{2\pi}\sqrt{\frac{g}{L_i}} $$
03

Find the frequency of pendulum B

Pendulum B has the same length as pendulum A, \(L_i\), but with a bob of mass \(2m\). Since the mass of the bob does not affect the frequency of a simple pendulum, the formula for the frequency of pendulum B is the same as for pendulum A. Hence, the frequency of pendulum B is: $$ f_B=\frac{1}{2\pi}\sqrt{\frac{g}{L_i}} $$
04

Compare the frequencies of small oscillations of the two pendulums

We can now compare the frequencies \(f_A\) and \(f_B\): Since both pendulums have the same length \(L_i\) and the mass of the bob does not affect their frequencies, their frequencies will be the same. $$ f_A=f_B $$ In conclusion, the frequencies of small oscillations of pendulums A and B are the same, regardless of the mass of their bobs.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Pendulum A has a bob of mass \(m\) hung from a string of length \(I_{i}\) pendulum \(B\) is identical to \(A\) except its bob has mass \(2 m\). Compare the frequencies of small oscillations of the two pendulums.

A mass of \(10.0 \mathrm{~kg}\) is hanging by a steel wire \(1.00 \mathrm{~m}\) long and \(1.00 \mathrm{~mm}\) in diameter. If the mass is pulled down slightly and released, what will be the frequency of the resulting oscillations? Young's modulus for steel is \(2.0 \cdot 10^{11} \mathrm{~N} / \mathrm{m}^{2}\)

A massive object of \(m=5.00 \mathrm{~kg}\) oscillates with simple harmonic motion. Its position as a function of time varies according to the equation \(x(t)=2 \sin ([\pi / 2] t+\pi / 6)\). a) What is the position, velocity, and acceleration of the object at \(t=0 \mathrm{~s}^{2}\) b) What is the kinetic energy of the object as a function of time? c) At which time after \(t=0 \mathrm{~s}\) is the kinetic energy first at a maximum?

A \(3.00-\mathrm{kg}\) mass attached to a spring with \(k=140 . \mathrm{N} / \mathrm{m}\) is oscillating in a vat of oil, which damps the oscillations. a) If the damping constant of the oil is \(b=10.0 \mathrm{~kg} / \mathrm{s}\), how long will it take the amplitude of the oscillations to decrease to \(1.00 \%\) of its original value? b) What should the damping constant be to reduce the amplitude of the oscillations by \(99.0 \%\) in 1.00 s?

A mass \(m\) is attached to a spring with a spring constant of \(k\) and set into simple harmonic motion. When the mass has half of its maximum kinetic energy, how far away from its equilibrium position is it, expressed as a fraction of its maximum displacement?
See all solutions

Recommended explanations on Physics Textbooks

Rotational Dynamics

Read Explanation

Torque and Rotational Motion

Read Explanation

Mechanics and Materials

Read Explanation

Further Mechanics and Thermal Physics

Read Explanation

Astrophysics

Read Explanation

Particle Model of Matter

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.