Answer
The answer and procedures of the exercise are attached in the following archives.
Step-by-step explanation:
You will find the procedures, formulas or necessary explanations in the archive attached below. If you have any question ask and I will aclare your doubts kindly.
Answer: D(t) =
Explanation: A harmonic motion of a spring can be modeled by a sinusoidal function, which, in general, is of the form:
y = or y =
where:
|a| is initil displacement
is period
For a Damped Harmonic Motion, i.e., when the spring doesn't bounce up and down forever, equations for displacement is:
or
For this question in particular, initial displacement is maximum at 8cm, so it is used the cosine function:
period =
12 =
ω =
Replacing values:
The equation of displacement, D(t), of a spring with damping factor is .
Answer:
See the answers below.
Explanation:
To solve this problem we must use the following equation of kinematics.
where:
Vf = final velocity = 10 [m/s]
Vo = initial velocity = 40 [m/s]
t = time = 5 [s]
a = acceleration [m/s²]
Now replacing:
Note: The negative sign in the above equation means that the velecity is decreasing.
2)
To solve this second part we must use the following equation of kinematics.
where:
x = distance [m]