Temperature and the period of a pendulum For oscillations of small amplitude (short swings), we may safely model the rela- tionship between the period T and the length L of a simple pen- dulum with the equation T = 27, where g is the constant acceleration of gravity at the pendulum's location. If we measure g in centimeters per second squared, we measure L in centimeters and T in seconds. If the pendulum is made of metal, its length will vary with temperature, either increas- ing or decreasing at a rate that is roughly proportional to L. In sym- bols, with u being temperature and k the proportionality constant, dL kL. du Assuming this to be the case, show that the rate at which the period changes with respect to temperature is kT/2.
Temperature and the period of a pendulum For oscillations of small amplitude (short swings), we may safely model the rela- tionship between the period T and the length L of a simple pen- dulum with the equation T = 27, where g is the constant acceleration of gravity at the pendulum's location. If we measure g in centimeters per second squared, we measure L in centimeters and T in seconds. If the pendulum is made of metal, its length will vary with temperature, either increas- ing or decreasing at a rate that is roughly proportional to L. In sym- bols, with u being temperature and k the proportionality constant, dL kL. du Assuming this to be the case, show that the rate at which the period changes with respect to temperature is kT/2.
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter1: Equations And Graphs
Section1.10: Modeling Variation
Problem 35E
Related questions
Question
Transcribed Image Text:Temperature and the period of a pendulum For oscillations
of small amplitude (short swings), we may safely model the rela-
tionship between the period T and the length L of a simple pen-
dulum with the equation
T = 27,
where g is the constant acceleration of gravity at the pendulum's
location. If we measure g in centimeters per second squared, we
measure L in centimeters and T in seconds. If the pendulum is
made of metal, its length will vary with temperature, either increas-
ing or decreasing at a rate that is roughly proportional to L. In sym-
bols, with u being temperature and k the proportionality constant,
dL
kL.
du
Assuming this to be the case, show that the rate at which the
period changes with respect to temperature is kT/2.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 4 images
Recommended textbooks for you
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
