Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf
Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf
9th Edition
ISBN: 9781259989452
Author: Hayt
Publisher: Mcgraw Hill Publishers
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Textbook Question
Chapter 17, Problem 1E

Determine the fundamental frequency, fundamental radian frequency, and period of the following: (a) 5 sin 9t; (b) 200 cos 70t; (c) 4 sin(4t − 10°); (d) 4 sin(4t + 10°).

(a)

Expert Solution
Check Mark
To determine

The fundamental frequency, fundamental angular frequency and period of the given function.

Answer to Problem 1E

The fundamental angular frequency of the given function is 9rad/s, fundamental frequency is 92πHz and the time period is 2π9s.

Explanation of Solution

Given data:

The given function f(t) is 5sin9t.

Calculation:

The general form of the function is given as,

f(t)=Asin(ω0t+ϕ)        (1)

Here,

A is the constant.

ω0 is the fundamental radian frequency.

ϕ is the phase angle of the function.

Compare the given function with equation (1).

The fundamental radian frequency is,

ω0=9rad/s

The fundamental frequency is given as,

f0=ω02π        (2)

Substitute 9rad/s for ω0 in the above equation.

f0=9rad/s2π=92πHz

The time period is given as,

T=1f0        (3)

Substitute 92πHz for f0 in the above equation.

T=192πHz=2π9s

Conclusion:

Therefore, the fundamental angular frequency of the given function is 9rad/s, fundamental frequency is 92πHz and the time period is 2π9s.

(b)

Expert Solution
Check Mark
To determine

The fundamental frequency, fundamental angular frequency and period of the given function

Answer to Problem 1E

The fundamental angular frequency of the given function is 70rad/s, fundamental frequency is 35πHz and the time period is π35s.

Explanation of Solution

Given data:

The given function f(t) is 200cos70t.

Calculation:

Compare the given function with equation (1).

The fundamental radian frequency is,

ω0=70rad/s

Substitute 70rad/s for ω0 in equation (2).

f0=70rad/s2π=35πHz

Substitute 35πHz for f0 in equation (3).

T=135πHz=π35s

Conclusion:

Therefore, the fundamental angular frequency of the given function is 70rad/s, fundamental frequency is 35πHz and the time period is π35s.

(c)

Expert Solution
Check Mark
To determine

The fundamental frequency, fundamental angular frequency and period of the given function

Answer to Problem 1E

The fundamental angular frequency of the given function is 4rad/s, fundamental frequency is 2πHz and the time period is π2s.

Explanation of Solution

Given data:

The given function f(t) is 4sin(4t10°).

Calculation:

Compare the given function with equation (1).

The fundamental radian frequency is,

ω0=4rad/s

Substitute 4rad/s for ω0 in equation (2).

f0=4rad/s2π=2πHz

Substitute 2πHz for f0 in equation (3).

T=12πHz=π2s

Conclusion:

Therefore, the fundamental angular frequency of the given function is 4rad/s, fundamental frequency is 2πHz and the time period is π2s.

(d)

Expert Solution
Check Mark
To determine

The fundamental frequency, fundamental angular frequency and period of the given function

Answer to Problem 1E

The fundamental angular frequency of the given function is 4rad/s, fundamental frequency is 2πHz and the time period is π2s.

Explanation of Solution

Given data:

The given function f(t) is 4sin(4t+10°).

Calculation:

Compare the given function with equation (1).

The fundamental radian frequency is,

ω0=4rad/s

Substitute 4rad/s for ω0 in equation (2).

f0=4rad/s2π=2πHz

Substitute 2πHz for f0 in equation (3).

T=12πHz=π2s

Conclusion:

Therefore, the fundamental angular frequency of the given function is 4rad/s, fundamental frequency is 2πHz and the time period is π2s.

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Chapter 17 Solutions

Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf

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