In a simple harmonic oscillator, if the mass is doubled, what happens to the tim

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Question: In a simple harmonic oscillator, if the mass is doubled, what happens to the time period? (2022)

Options:

Correct Answer: It doubles

Exam Year: 2022

Solution:

Time period (T) = 2π√(m/k), doubling m will double T.

In a simple harmonic oscillator, if the mass is doubled, what happens to the time period? (2022)

In a simple harmonic oscillator, if the mass is doubled, what happens to the time period? (2022)

Step 1: Understand the formula for the time period (T) of a simple harmonic oscillator, which is T = 2π√(m/k).
Step 2: Identify the variables in the formula: m is the mass and k is the spring constant.
Step 3: Note that if the mass (m) is doubled, we replace m with 2m in the formula.
Step 4: Substitute 2m into the formula: T = 2π√(2m/k).
Step 5: Simplify the equation: T = 2π√(2)√(m/k).
Step 6: Recognize that √(2) is a constant factor, so the new time period is T = √(2) * (2π√(m/k)).
Step 7: Conclude that the time period increases by a factor of √(2), which means it does not simply double, but increases by a factor related to the square root of 2.

Simple Harmonic Motion – Understanding the relationship between mass, spring constant, and time period in a simple harmonic oscillator.
Time Period Formula – Application of the formula T = 2π√(m/k) to analyze how changes in mass affect the time period.