Respuesta :
Answer:
X (t) = 60 cos 4t
Explanation:
When this system is released, a simple harmonic movement began, which is described by the equations
x = A cos (wt + fi)
Angular velocity is
w = ra K / m
w = RA 64/4
w = 4 rad / s
To find the phase angle (fi) we use the condition that gives leaves of rest for x = 0
Let's find the speed
v = dx / de
v = A w sin (wt + fi)
0 = A w sin (0+ fi)
Therefore the value of fi = 0
To find the amplitude let's use the acceleration of the system
.a = dv / dt
.a = A w2 cos wt
If we use Newton's second law
F = m a
240 e -4t cos 4t = a w2 cos wt
At the initial time t = 0
240 = a w2
.a = 240 / w2
.a = 240/42
.a = 60
The equation remains
X (t) = 60 cos 4t
The equation of the motion in the absence of damping should be X (t) = 60 cos 4t.
Calculation of the equation:
At the time when the system should be released so here the harmonic movement started by the following equation
x = A cos (wt + fi)
Now
Angular velocity is
w = ra K / m
w = RA 64/4
w = 4 rad / s
Now determine the speed
v = dx / de
v = A w sin (wt + fi)
0 = A w sin (0+ fi)
So, the value of fi = 0
Now the acceleration of the system
.a = dv / dt
.a = A w2 cos wt
Here we used Newton's second law
F = m a
= 240 e -4t cos 4t
= a w2 cos wt
At the initial time t = 0
So,
240 = a w2
a = 240 / w2
a = 240/42
a = 60
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