Question

Question 2 (3 points) A mass hangs from a spring and moves in simple harmonic motion. How does the period of oscillation change when the mass is increased by a factor of 4?

Answer 1

Consider that the initial time period of oscillation is T,
T = 2$\pi$ SQRT[m/k]
Where m is the mass and k is the spring constant
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Consider the new time period as T'
T' = 2$\pi$ * SQRT[4m / k] [m become 4m]
= 2 * {2$\pi$ * SQRT[m / k]
= 2 * T
So, when mass increases by a factor of 4, the time period increase by a factor of 2.