If the mass of a simple harmonic oscillator is doubled while keeping the spring constant the same, how does the period change?

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Q: If the mass of a simple harmonic oscillator is doubled while keeping the spring constant the same, how does the period change?

Solution: The period T = 2π√(m/k). If m is doubled, T increases.

Steps: 7

Step 1: Understand the formula for the period of a simple harmonic oscillator, which is T = 2π√(m/k).
Step 2: Identify the variables in the formula: T is the period, m is the mass, and k is the spring constant.
Step 3: Note that in this scenario, the spring constant k remains the same.
Step 4: Recognize that if the mass m is doubled, we can represent the new mass as 2m.
Step 5: Substitute the new mass into the formula: T' = 2π√(2m/k).
Step 6: Simplify the new period: T' = 2π√(2) * √(m/k) = √(2) * T.
Step 7: Conclude that since √(2) is greater than 1, the new period T' is greater than the original period T.