If the mass of a simple harmonic oscillator is tripled, how does the frequency c

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Question: If the mass of a simple harmonic oscillator is tripled, how does the frequency change?

Options:

Correct Answer: It is reduced to one-third

Solution:

The frequency f is inversely proportional to the square root of the mass m, so if m is tripled, the frequency is reduced to one-third.

If the mass of a simple harmonic oscillator is tripled, how does the frequency change?

If the mass of a simple harmonic oscillator is tripled, how does the frequency change?

Step 1: Understand that a simple harmonic oscillator's frequency (f) is related to its mass (m).
Step 2: Know the formula for frequency in a simple harmonic oscillator: f = 1/(2π) * √(k/m), where k is the spring constant.
Step 3: Recognize that frequency (f) is inversely proportional to the square root of the mass (m). This means that if mass increases, frequency decreases.
Step 4: If the mass (m) is tripled, we can express this as m' = 3m, where m' is the new mass.
Step 5: Substitute the new mass into the frequency formula: f' = 1/(2π) * √(k/(3m)).
Step 6: Notice that √(1/3) is the same as 1/√3, which means the new frequency f' = f/√3.
Step 7: Since √3 is approximately 1.732, the frequency is reduced to about 0.577 times the original frequency, not one-third.

Simple Harmonic Motion – The relationship between mass and frequency in a simple harmonic oscillator, where frequency is inversely proportional to the square root of mass.