Exponential decay of a pendulum oscillation amplitude

In summary, the conversation discusses using ln to simplify a solution for a problem. The property of ln is referenced and applied to the right side of the equation, resulting in the elimination of Ae. The conversation also mentions the property that ln of a power is equal to the power multiplied by ln of the base.
  • #1
asilvester635
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Homework Statement


I found an answer on the internet for this problem, but I'm not sure on one of the steps. The solution says, "Take ln of both sides to get rid of Ae. If we do that, then the right side will be ln(Ae^t/T). I don't see how using ln will get rid of Ae?

Homework Equations


Refer to the image in part 3.

The Attempt at a Solution


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  • #2
Hi, I remember you the property of ##\ln##:

##\ln{(A\cdot B)} \,=\, \ln{A}+\ln{B}##

apply this to the right side ## \ln{(Ae^{-\frac{t}{T}})}##, what is the result ?

Ps. remember also that ##\ln{(A^B)}=B\ln{A}##.
Ssnow
 

Related to Exponential decay of a pendulum oscillation amplitude

1. What is exponential decay in the context of a pendulum oscillation amplitude?

Exponential decay refers to the gradual decrease in amplitude of a pendulum's oscillation over time. This is caused by factors such as air resistance and friction, which dampen the motion of the pendulum.

2. How does the length of a pendulum affect the rate of exponential decay?

The longer the length of a pendulum, the slower the rate of exponential decay. This is because longer pendulums have a larger swing radius, which results in less resistance and therefore less dampening of the oscillation.

3. Can the mass of a pendulum affect the rate of exponential decay?

Yes, the mass of a pendulum can affect the rate of exponential decay. Generally, a heavier pendulum will experience more resistance and friction, leading to a faster decay of its oscillation amplitude.

4. How does the environment affect the exponential decay of a pendulum's oscillation amplitude?

The environment, specifically factors such as air resistance and humidity, can greatly impact the rate of exponential decay of a pendulum's oscillation amplitude. These external forces can add resistance and friction, causing the pendulum to lose energy faster.

5. Is it possible for a pendulum's oscillation amplitude to reach zero due to exponential decay?

No, a pendulum's oscillation amplitude will never reach zero due to exponential decay. This is because the decay follows an exponential curve, meaning that the amplitude will approach but never reach zero.

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