In a simple harmonic oscillator, if the mass is doubled, what happens to the time period? (2022)
Practice Questions
1 question
Q1
In a simple harmonic oscillator, if the mass is doubled, what happens to the time period? (2022)
It remains the same
It doubles
It increases by √2
It decreases by √2
Time period (T) = 2π√(m/k), doubling m will double T.
Questions & Step-by-step Solutions
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Q
Q: In a simple harmonic oscillator, if the mass is doubled, what happens to the time period? (2022)
Solution: Time period (T) = 2π√(m/k), doubling m will double T.
Steps: 7
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.
