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Question 4 The period of a clock pendulum T is given by the equation T = 2ñ1 L where the constant L is the length of the pendulum and g is the acceleration due to gravity. The period of the clock pendulum varies slightly depending on where it is located on earth's surface, due to small changes in g. (a) If g increases, will T increase or decrease? Does this correspond to the clock pendulum speeding up or slowing down? Explain your reasoning. (b) Find the linear approximation for T(g) centered at g = 980 cm/sec², if the length of the pendulum is 400 cm. (c) When a clock with a 400 cm pendulum is moved from a location where g = 980 cm/sec? to a new location, its period increases by .001sec. Estimate the amount by which g increases and approximate the value of g at the new location.

Question 4 The period of a clock pendulum T is given by the equation T = 2ñ1 L where the constant L is the length of the pendulum and g is the acceleration due to gravity. The period of the clock pendulum varies slightly depending on where it is located on earth's surface, due to small changes in g. (a) If g increases, will T increase or decrease? Does this correspond to the clock pendulum speeding up or slowing down? Explain your reasoning. (b) Find the linear approximation for T(g) centered at g = 980 cm/sec², if the length of the pendulum is 400 cm. (c) When a clock with a 400 cm pendulum is moved from a location where g = 980 cm/sec? to a new location, its period increases by .001sec. Estimate the amount by which g increases and approximate the value of g at the new location.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Question 4** The period of a clock pendulum \( T \) is given by the equation \( T = 2\pi \sqrt{\frac{L}{g}} \) where the constant \( L \) is the length of the pendulum and \( g \) is the acceleration due to gravity. The period of the clock pendulum varies slightly depending on where it is located on Earth's surface, due to small changes in \( g \). (a) If \( g \) increases, will \( T \) increase or decrease? Does this correspond to the clock pendulum speeding up or slowing down? Explain your reasoning. (b) Find the linear approximation for \( T(g) \) centered at \( g = 980 \, \text{cm/sec}^2 \), if the length of the pendulum is 400 cm. (c) When a clock with a 400 cm pendulum is moved from a location where \( g = 980 \, \text{cm/sec}^2 \) to a new location, its period increases by 0.001 sec. Estimate the amount by which \( g \) increases and approximate the value of \( g \) at the new location.
Transcribed Image Text:**Question 4** The period of a clock pendulum \( T \) is given by the equation \( T = 2\pi \sqrt{\frac{L}{g}} \) where the constant \( L \) is the length of the pendulum and \( g \) is the acceleration due to gravity. The period of the clock pendulum varies slightly depending on where it is located on Earth's surface, due to small changes in \( g \). (a) If \( g \) increases, will \( T \) increase or decrease? Does this correspond to the clock pendulum speeding up or slowing down? Explain your reasoning. (b) Find the linear approximation for \( T(g) \) centered at \( g = 980 \, \text{cm/sec}^2 \), if the length of the pendulum is 400 cm. (c) When a clock with a 400 cm pendulum is moved from a location where \( g = 980 \, \text{cm/sec}^2 \) to a new location, its period increases by 0.001 sec. Estimate the amount by which \( g \) increases and approximate the value of \( g \) at the new location.
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