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

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

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

Steps: 6

Step 1: Understand that simple harmonic motion involves a mass attached to a spring.
Step 2: Know that the period (T) is the time it takes for one complete cycle of motion.
Step 3: Remember the formula for the period of a mass-spring system: T = 2π√(m/k), where m is the mass and k is the spring constant.
Step 4: Identify that if the mass (m) increases while the spring constant (k) stays the same, the value of m in the formula increases.
Step 5: Realize that as m increases, the square root of m (√m) also increases, which makes T larger.
Step 6: Conclude that the period (T) increases when the mass is increased.