the amplitude of an oscillator decreases to 36.8% of its initial value in 10.0 s. what is the value of the time constant

τ = 5 s

Explanation:

When a vibrating body is damped. Its amplitude starts to decrease. This decrement is exponential. And it is given as follows:

where,

τ = Time Constant = ?

X = Instantaneous value of amplitude

X₀ = Initial Value of amplitude

t = time interval = 10 s

The ratio of decrement is given as:

therefore, using these values, we get:

Taking natural log (ln) on both sides, we get:

τ = 5 s

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