Modeling with periodic functions: Cyclical exponential decay. A spring is attached to the ceiling and pulled 17 cm down from equilibrium and released. After 4 seconds the amplitude has decreased to 10 cm. Also, the spring oscillates 12 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) = 17(0.87577)* - cos(24rt) . [Note: Here we define t as the number of seconds elapsed. Also, locations below the resting position have negative values for D.] 6 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
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
![Modeling with periodic functions: Cyclical exponential decay. A spring is
attached to the ceiling and pulled 17 cm down from equilibrium and released.
After 4 seconds the amplitude has decreased to 10 cm. Also, the spring oscillates
12 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) = 17(0.87577)' · cos(24rt) .
[Note: Here we define t as the number of seconds elapsed. Also, locations below
the resting position have negative values for D.]
After t = 6 seconds, how far from equilibrium is the end of the spring?
your answer is a decimal, please round to no more than 3 decimal places.
cm](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc2155a63-9e9a-4eeb-b35a-52db10fb6e33%2F5acc08df-ce77-42f0-b539-cc2e50b816cc%2Fapew7hl_processed.png&w=3840&q=75)
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