Modeling with periodic functions: Cyclical exponential decay. A spring is attached to the ceiling and pulled 11 cm down from equilibrium and released. After 4 seconds the amplitude has decreased to 7 cm. Also, the spring oscillates 13 times each second. Assuming that the amplitude is decreasing exponentially, below is a model for the distance, D the end of the spring is below equilibrium, in terms of seconds, t: D(t) = 11(0.89315)* . cos(26nt) . [Note: Here we define t as the number of seconds elapsed. Also, locations below the resting position have negative values for D.] 8 seconds, how far from equilibrium is the end of the spring? If your answer is a decimal, please round to no more than 3 decimal places. After t cm
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
![Modeling with periodic functions: Cyclical exponential decay. A spring is
attached to the ceiling and pulled 11 cm down from equilibrium and released.
After 4 seconds the amplitude has decreased to 7 cm. Also, the spring oscillates
13 times each second. Assuming that the amplitude is decreasing exponentially,
below is a model for the distance, D the end of the spring is below equilibrium,
in terms of seconds, t:
D(t) = 11(0.89315)* . cos(26nt) .
[Note: Here we define t as the number of seconds elapsed. Also, locations below
the resting position have negative values for D.]
8 seconds, how far from equilibrium is the end of the spring?
If your answer is a decimal, please round to no more than 3 decimal places.
After t
cm](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe97891cc-55dd-4114-b40f-d7abbb3547ef%2F887d3eab-1493-480a-a630-22098bfa1c93%2F0cal29a_processed.png&w=3840&q=75)
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