In a harmonic oscillator, if the mass is doubled while keeping the spring consta

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Question: In a harmonic oscillator, if the mass is doubled while keeping the spring constant the same, how does the frequency change? (2021)

Options:

Correct Answer: Decreases

Exam Year: 2021

Solution:

Frequency (f) = (1/2π)√(k/m). If mass (m) is doubled, frequency decreases.

In a harmonic oscillator, if the mass is doubled while keeping the spring constant the same, how does the frequency change? (2021)

In a harmonic oscillator, if the mass is doubled while keeping the spring constant the same, how does the frequency change? (2021)

Step 1: Understand the formula for frequency of a harmonic oscillator, which is f = (1/2π)√(k/m).
Step 2: Identify the variables in the formula: f is frequency, k is the spring constant, and m is the mass.
Step 3: Note that in this scenario, the spring constant (k) remains the same.
Step 4: Recognize that if the mass (m) is doubled, we replace m with 2m in the formula.
Step 5: Substitute 2m into the frequency formula: f = (1/2π)√(k/(2m)).
Step 6: Simplify the equation: f = (1/2π)√(k/2m) = (1/2) * (1/2π)√(k/m).
Step 7: Conclude that the new frequency is (1/√2) times the original frequency, which means the frequency decreases.

Harmonic Oscillator – A system that experiences restoring forces proportional to the displacement from equilibrium, characterized by its mass and spring constant.
Frequency of Oscillation – The rate at which an oscillator completes a cycle, inversely related to the square root of mass in a harmonic oscillator.
Effect of Mass on Frequency – Doubling the mass of a harmonic oscillator results in a decrease in frequency, as frequency is inversely proportional to the square root of mass.