**Problem 4:** The period, \( T \) (in seconds) of a simple pendulum as a function of its length, \( L \) (in feet) is given by \[ T(L) = 2\pi \sqrt{\frac{L}{32.2}} \] **(a)** Input quantity: ___________ and Output quantity: ___________ **(b)** Evaluate: \( T(3.5) \) and describe what this means in a sentence. **(c)** For the INVERSE FUNCTION what is the Input quantity: ___________ and Output quantity: ___________ **(d)** Find \( T^{-1}(L) \) (the inverse function) **(e)** Evaluate \( T^{-1}(3) \) and describe what this means in a sentence.
**Problem 4:** The period, \( T \) (in seconds) of a simple pendulum as a function of its length, \( L \) (in feet) is given by \[ T(L) = 2\pi \sqrt{\frac{L}{32.2}} \] **(a)** Input quantity: ___________ and Output quantity: ___________ **(b)** Evaluate: \( T(3.5) \) and describe what this means in a sentence. **(c)** For the INVERSE FUNCTION what is the Input quantity: ___________ and Output quantity: ___________ **(d)** Find \( T^{-1}(L) \) (the inverse function) **(e)** Evaluate \( T^{-1}(3) \) and describe what this means in a sentence.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Problem 4:**
The period, \( T \) (in seconds) of a simple pendulum as a function of its length, \( L \) (in feet) is given by
\[
T(L) = 2\pi \sqrt{\frac{L}{32.2}}
\]
**(a)** Input quantity: ___________ and Output quantity: ___________
**(b)** Evaluate: \( T(3.5) \) and describe what this means in a sentence.
**(c)** For the INVERSE FUNCTION what is the Input quantity: ___________ and Output quantity: ___________
**(d)** Find \( T^{-1}(L) \) (the inverse function)
**(e)** Evaluate \( T^{-1}(3) \) and describe what this means in a sentence.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5cf437dc-af80-404d-8013-877ac047e694%2F5532df95-10b2-43ee-8120-e63ad9c0556d%2Fqz2rv5e.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 4:**
The period, \( T \) (in seconds) of a simple pendulum as a function of its length, \( L \) (in feet) is given by
\[
T(L) = 2\pi \sqrt{\frac{L}{32.2}}
\]
**(a)** Input quantity: ___________ and Output quantity: ___________
**(b)** Evaluate: \( T(3.5) \) and describe what this means in a sentence.
**(c)** For the INVERSE FUNCTION what is the Input quantity: ___________ and Output quantity: ___________
**(d)** Find \( T^{-1}(L) \) (the inverse function)
**(e)** Evaluate \( T^{-1}(3) \) and describe what this means in a sentence.
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