The time period of a simple harmonic oscillator is given by T = 2π√(m/k). If the mass is doubled, what will be the new time period?

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Q: The time period of a simple harmonic oscillator is given by T = 2π√(m/k). If the mass is doubled, what will be the new time period?

Solution: If the mass is doubled, the new time period T' = 2π√(2m/k) = √2 * (2π√(m/k)) = √2 * T. Thus, the time period increases.

Steps: 7

Step 1: Start with the formula for the time period of a simple harmonic oscillator, T = 2π√(m/k).
Step 2: Identify that 'm' is the mass and 'k' is the spring constant.
Step 3: If the mass is doubled, replace 'm' with '2m' in the formula.
Step 4: Write the new time period formula: T' = 2π√(2m/k).
Step 5: Factor out the square root: T' = 2π√(2) * √(m/k).
Step 6: Recognize that √(m/k) is the original time period T, so T' = √2 * T.
Step 7: Conclude that the new time period T' is √2 times the original time period T, meaning it increases.