Find the Domain w = square root of k/m

Problem

w=√(,k/m)

Solution

1. Identify the restriction for a square root function. For the expression to be a real number, the radicand must be non-negative.

k/m≥0

2. Analyze the fraction. A fraction is non-negative if both the numerator and denominator have the same sign, or if the numerator is zero.

(k≥0* and *m>0)* or *(k≤0* and *m<0)

3. Exclusion of zero in the denominator. Since division by zero is undefined, the variable m cannot be equal to zero.

m≠0

4. Determine the domain in terms of the variables k and m In many physical contexts (like a mass-spring system), k and m are assumed to be positive, but mathematically, the domain includes all pairs (k,m) where the ratio is non-negative and m is non-zero.

Domain={(k,m)∈ℝ^2:k/m≥0,m≠0}

Final Answer

Domain={(k,m):(k≥0* and *m>0)* or *(k≤0* and *m<0)}

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