Precalculus: Mathematics for Calculus - 6th Edition
6th Edition
ISBN: 9780840068071
Author: Stewart, James, Redlin, Lothar, Watson, Saleem
Publisher: Cengage Learning
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Textbook Question
Chapter 5.6, Problem 1E
For an object in simple harmonic motion with amplitude a and period 2π/ω, find an equation that models the displacement y at time t if
- (a) y = 0 at time t = 0: y = __________.
- (b) y = a at time t = 0: y = __________.
(a)
Expert Solution
To determine
To fill: The equation for the displacement of the object in simple harmonic motion.
Answer to Problem 1E
The equation for the displacement of the object in simple harmonic motion is
Explanation of Solution
Given:
The displacement y is 0 at time
Definition used:
The equation for the simple harmonic motion which describes the displacement y of an object at time t is,
If both the equation are satisfied, then the object is said to be in simple harmonic motion.
Where,
Amplitude is equal to
Period is equal to
Frequency is equal to
Calculation:
From the definition of the simple harmonic motion, displacement can be written as,
The displacement y is 0 at
Substitute the value 0 for t, in equation (1),
Thus, the displacement is 0 at time
Now, substitute the value 0 for t in equation (2),
Thus, the value of displacement is a for the time
Hence the equation for the displacement of the models of simple harmonic motion at time
(b)
Expert Solution
To determine
To fill: The equation for the displacement of the object in simple harmonic motion.
Answer to Problem 1E
The equation for the displacement of the object in simple harmonic motion is
Explanation of Solution
Given:
The displacement y is a at time
Definition used:
The equation for the simple harmonic motion which describes the displacement y of an object at time t is,
If both the equation are satisfied, then the object is said to be in simple harmonic motion.
Where,
Amplitude is equal to
Period is equal to
Frequency is equal to
Calculation:
From the definition of the simple harmonic motion, displacement can be written as,
The displacement y is a at
Substitute the value 0 for t, in equation (1),
Thus, the displacement is 0 at time
Now, substitute the value 0 for t in equation (2),
Thus, the value of displacement is a for the time
Hence the equation for the displacement a of the object in simple harmonic motion at time
Chapter 5 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
Ch. 5.1 - Prob. 1ECh. 5.1 - Prob. 2ECh. 5.1 - Prob. 3ECh. 5.1 - Prob. 4ECh. 5.1 - Prob. 5ECh. 5.1 - Prob. 6ECh. 5.1 - Prob. 7ECh. 5.1 - Prob. 8ECh. 5.1 - Prob. 9ECh. 5.1 - Prob. 10E
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