Concept explainers
(a)
To find: The derivative
(a)
Answer to Problem 32SP
Explanation of Solution
Given information:
Consider the equation,
Calculation:
The position of the object attached to the spring is,
Differentiating
The rate of change of position of object represents velocity
(b)
To find: The second derivative
(b)
Answer to Problem 32SP
Explanation of Solution
Given information:
Consider the equation,
Calculation:
The position of the object attached to the spring is,
Differentiating
The rate of change of velocity of object represents velocity
(c)
To find: The position and velocity at
(c)
Answer to Problem 32SP
Explanation of Solution
Given information:
Consider the equation,
Calculation:
The position of the object attached to the spring is,
Substitute
Hence,
(d)
To find: The position and velocity at
(d)
Answer to Problem 32SP
Explanation of Solution
Given information:
Consider the equation,
Calculation:
The position of the object attached to the spring is,
Substitute
Hence,
(e)
To find: The position and velocity at
(e)
Answer to Problem 32SP
Explanation of Solution
Given information:
Consider the equation,
Calculation:
The position of the object attached to the spring is,
Substitute
Hence,
(f)
To find: The differential equation does the object follows.
(f)
Answer to Problem 32SP
Explanation of Solution
Given information:
Consider the equation,
Calculation:
The position of the object attached to the spring is,
Thus the differential equation is
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