Harmonic movement of a spring question

AI Thread Summary
To calculate the force exerted by a spring on a mass at any moment, the acceleration formula a = -A*w^2*sin(wt + u) is used, where A is the amplitude and w is the angular frequency. The phase angle "u" is questioned, specifically why it is set to pi/4 in this context. The initial conditions lead to the equations r(t) = A*sin(wt + u) and r(0) = A, which help determine the phase angle based on the position of the mass. Visualizing the unit circle can clarify that pi/4 corresponds to specific initial positions of the mass. Understanding the phase angle is crucial for accurately modeling the harmonic motion of the spring-mass system.
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i got a mass "m" which is stuck to a spring which is hanged from the sealing .
k-the spring coefficient
the formula for acceleration is

a=-A*w^2*sin(wt+u)
i need to calculate the force which the spring exerts of the mass in any given moment
t=0 is when he was moved downward by distance A (amplitude) to some amplitude and released.

my main question is why the phase angle "u" is pi/4 ??
 
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Your initial conditions gives these equations, from which you should be able to retrieve u:
r(t)=Asin(wt+u)
r(0)=A
 
my main question is why the phase angle need to be pi/4 ??
how do i count the phrase angle in this string situation
just by viewing the location of the object.
 
m is mass
+ is the point of balance
what is the phase angle if we start counting from this position?
+
|
|
m
 
Imagine the unit circle projected onto the y-axis, then pi/4 corresponds to 1, 0 and pi to 0 and -pi/4 to -1 as initial positions.
 
i can't image what you say
can you draw it??
 
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