Coupled oscillation problem, describing subsequent motion

In summary, the string with no initial displacement and an initial velocity v_0 will undergo coupled oscillations, with a node at the center and two antinodes at the ends. The velocity of the nodes and antinodes will be v = v_0 / 2 and the displacement of any point on the string at any time t is given by x(t) = v_0 t sin (kx) where k = π/2s. The velocity of the string at any point in time is v(t) = v_0 cos (kx).
  • #1
lark0901
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Homework Statement



A string with no initial displacement is set into motion by being struck over a length 2s about its center. This center section is given an initial velocity v_0. Describe the subsequent motion.

Homework Equations



Coupled oscillations...

The Attempt at a Solution


I've managed to solve to a particular point, but I can't go any further..
And I'm not sure of whether I am doing right, so ..I need help!
 
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  • #2
The string will begin to vibrate as a result of the initial velocity given to it. The subsequent motion will be a coupled oscillation, with a node at the center and two antinodes at the ends of the string. The nodes and antinodes will move along the string with a velocity v, which is given by the equation v = v_0 / 2 The displacement of any point on the string at any time t is given by the equation x(t) = v_0 t sin (kx) where k = π/2s is the wave number. At any point in time, the velocity of the string at that point is given by v(t) = v_0 cos (kx)
 

Related to Coupled oscillation problem, describing subsequent motion

1. What is a coupled oscillation problem?

A coupled oscillation problem is a type of physical system in which two or more oscillators are connected and influence each other's motion. This can result in complex and interesting patterns of motion.

2. How do you describe the subsequent motion in a coupled oscillation problem?

The subsequent motion in a coupled oscillation problem can be described using mathematical equations. These equations take into account the initial conditions of the system, as well as the properties of the oscillators and the coupling between them.

3. What factors can affect the motion in a coupled oscillation problem?

The motion in a coupled oscillation problem can be affected by various factors such as the strength of the coupling between the oscillators, the masses and spring constants of the oscillators, and any external forces acting on the system.

4. How does the number of oscillators affect the behavior of a coupled oscillation problem?

The number of oscillators in a coupled oscillation problem can greatly impact the behavior of the system. With more oscillators, the motion can become more complex and chaotic, while fewer oscillators may result in simpler and more predictable motion.

5. Can coupled oscillation problems be found in real-world applications?

Yes, coupled oscillation problems can be found in various real-world applications such as pendulum clocks, musical instruments, and even in the behavior of certain chemical reactions. They are also commonly used in the study of waves, vibrations, and other physical phenomena.

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