You are watching a mass oscillate on a spring. The initial amplitude is 40 cm. T

Question

You are watching a mass oscillate on a spring. The initial amplitude is 40 cm. The amplitude halves after 10 s. How long does it take for the amplitude of the oscillation to decrease to 5 cm?

*I feel like it would be 30 seconds, simply because you'd half it 3 times, taking 10 seconds each time. But I want to make sure that it correct, and more importantly, that the REASONING behind that is correct. Just want to see a formula to kind of back it up. I am aware this is a very easy question, but I'm 100% new to physics.

Explanation / Answer

Use damping oscillator equation

A = A0 exp(-bt/2m)

The amplitude halves after 10 s

As, it exponentially decay, after 10 s, the amplitude is 40 cm /2 = 20 cm

In next 10 s, it will be 20 cm/2 = 10 cm

Next 10 s, it will be 10 cm /2 = 5 cm

Thus, it will be 5cm after 10 s + 10 s +10 s = 30 s

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