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The amplitude of a lightly damped harmonic oscillator decreases from 60.0 cm to 40.0 cm in 10.0 s. What will be the amplitude of the harmonic oscillator after another 10.0 s passes?

User Rents
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Final answer:

In a lightly damped harmonic oscillator, the amplitude decreases over time due to the effects of damping. To calculate the amplitude after another 10.0 s, we can use the exponential decay model and solve for the damping coefficient.

Step-by-step explanation:

In a lightly damped harmonic oscillator, the amplitude decreases over time due to the effects of damping. In this case, the amplitude decreases from 60.0 cm to 40.0 cm in 10.0 s. We can assume that the decrease in amplitude follows an exponential decay model. We can use the formula:

A(t) = A0 * e^(-bt)

Where A(t) is the amplitude after time t, A0 is the initial amplitude, b is the damping coefficient, and e is Euler's number (approximately 2.71828). From the given information, we can plug in the values to solve for b:

40.0 = 60.0 * e^(-10.0b)

After finding the value of b, we can use the same formula to find the amplitude after another 10.0 s passes.

User Kaqqao
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