In a simple harmonic oscillator, if the mass is increased while keeping the spring constant the same, what happens to the period?

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Q: In a simple harmonic oscillator, if the mass is increased while keeping the spring constant the same, what happens to the period?

Solution: The period T = 2π√(m/k) increases with an increase in mass (m).

Steps: 6

Step 1: Understand what a simple harmonic oscillator is. It consists of a mass attached to a spring that moves back and forth.
Step 2: Know the formula for the period (T) of a simple harmonic oscillator: T = 2π√(m/k), where m is the mass and k is the spring constant.
Step 3: Identify that in this question, the spring constant (k) remains the same while the mass (m) is increased.
Step 4: Recognize that increasing the mass (m) will affect the value inside the square root in the formula.
Step 5: Realize that as mass (m) increases, the value of √(m/k) also increases because k is constant.
Step 6: Conclude that since T is directly proportional to √(m/k), an increase in mass (m) will lead to an increase in the period (T).