Uncategorized: Practice Problem & Solution
The amplitude of oscillations is reduced to half of its initial value of 40 cm due to damping by resistive force in time \(t_0\), then after time \(3t_0\), its amplitude will be
Solution Explained:
To solve this problem, we apply the core principles of Uncategorized. Understanding the underlying formula is key to arriving at the correct answer below:
Damped amplitude is given by \(A = A_0 e^{-\gamma t}\). Here \(e^{-\gamma t_0} = 1/2\). For \(t = 3t_0\), \(A = A_0 (e^{-\gamma t_0})^3 = 40 \times (1/2)^3 = 5\text{ cm}\).
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