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Which of the following is true if the damping constant of an oscillator, b, decreases? The time constant, τ, is unaffected. The time constant, τ, decreases. The time constant, τ, increases.

Question

Which of the following is true if the damping constant of an oscillator, b, decreases? The time constant, τ, is unaffected. The time constant, τ, decreases. The time constant, τ, increases.

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Solution

The time constant, τ, increases.

Here's why:

The time constant of an oscillator is inversely proportional to the damping constant. This means that if the damping constant, b, decreases, the time constant, τ, will increase.

This is because the damping constant measures the amount of resistance an oscillator experiences. A lower damping constant means less resistance, which allows the oscillator to continue for a longer period of time. This longer duration is reflected in a larger time constant.

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