Harmonic movement of a spring question

In summary, the conversation discusses the calculation of force exerted by a spring on a mass hanging from the ceiling. The formula for acceleration is a=-A*w^2*sin(wt+u) and the phase angle "u" is being questioned as to why it is pi/4. The speaker suggests retrieving the phase angle from initial conditions and explains how it corresponds to different positions on a unit circle projected onto the y-axis. The listener requests a visual representation of this explanation.
  • #1
transgalactic
1,395
0
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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  • #2
Your initial conditions gives these equations, from which you should be able to retrieve u:
r(t)=Asin(wt+u)
r(0)=A
 
  • #3
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.
 
  • #4
m is mass
+ is the point of balance
what is the phase angle if we start counting from this position?
+
|
|
m
 
  • #5
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.
 
  • #6
i can't image what you say
can you draw it??
 

Related to Harmonic movement of a spring question

1. What is harmonic movement of a spring?

The harmonic movement of a spring refers to the oscillatory motion of a spring when it is under the influence of a restoring force that is directly proportional to its displacement from its equilibrium position. This type of movement is also known as simple harmonic motion.

2. What factors affect the harmonic movement of a spring?

The harmonic movement of a spring is affected by several factors such as the mass of the object attached to the spring, the stiffness of the spring, and the amplitude of the oscillations. The gravitational force and air resistance may also have an impact on the movement.

3. How is the period of harmonic movement of a spring calculated?

The period of harmonic movement of a spring can be calculated using the equation T = 2π√(m/k), where T is the period, m is the mass of the object attached to the spring, and k is the spring constant.

4. What is the difference between simple harmonic motion and damped harmonic motion?

Simple harmonic motion is the ideal type of harmonic movement of a spring, where there is no external force or resistance to the motion. Damped harmonic motion, on the other hand, occurs when there is an external force or resistance that causes the amplitude of the oscillations to decrease over time.

5. How is the harmonic movement of a spring used in real-life applications?

The harmonic movement of a spring is used in various real-life applications such as in clocks, watches, and musical instruments. It is also used in shock absorbers for vehicles and in suspension systems for buildings and bridges to reduce the impact of vibrations and oscillations.

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