How Do Initial Conditions Affect Oscillations in a 10 Mass-Spring System?

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In summary, a mass-spring undamped system is a physical system with a mass attached to a spring and no external forces or damping. The mass is pulled down by gravity, creating a restoring force that causes oscillatory motion. The equation of motion is m(d^2x/dt^2) + kx = 0, where m is the mass, k is the spring constant, x is the displacement, and t is time. The mass affects the natural frequency and amplitude of the oscillations. Energy is conserved in this system due to the constant conversion between kinetic and potential energy.
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wavey_simon
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Hello!

I've been calculating the eigenvalues and eigenvectors for a 10 mass-spring system. If you are given some initial displacement and velocity conditions, what are the resulting oscillations?

dot or vector product of normal nodes? superposition of normal modes? etc

thanks if anyone can help me out
 
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  • #2
10? that's enough to notice wave *propagation*, as well as the standing-waves that correspond to the normal modes.
 
  • #3
yeah but assuming you don't notice propagation. just need to know how you calculate the resulting oscillation

ty
 

Related to How Do Initial Conditions Affect Oscillations in a 10 Mass-Spring System?

1. What is a mass-spring undamped system?

A mass-spring undamped system is a physical system that consists of a mass attached to a spring, with no external forces or damping present. It is a simple model often used in physics to study the behavior of oscillating systems.

2. How does a mass-spring undamped system work?

In a mass-spring undamped system, the mass is pulled down by gravity, causing the spring to stretch. This stretching creates a restoring force that pulls the mass back up, resulting in oscillatory motion. The mass will continue to oscillate at its natural frequency until an external force or damping is introduced.

3. What is the equation of motion for a mass-spring undamped system?

The equation of motion for a mass-spring undamped system is given by:
m(d^2x/dt^2) + kx = 0
where m is the mass, k is the spring constant, x is the displacement of the mass, and t is time.

4. How does the mass affect the behavior of a mass-spring undamped system?

The mass in a mass-spring undamped system affects the natural frequency of oscillation. A larger mass will result in a lower natural frequency, meaning the oscillations will be slower. The mass also affects the amplitude of the oscillations, with a larger mass resulting in a larger amplitude.

5. How is energy conserved in a mass-spring undamped system?

In a mass-spring undamped system, energy is conserved because there are no external forces or damping present. The energy is constantly being converted between kinetic energy (from the motion of the mass) and potential energy (from the stretching of the spring). This results in the mass-spring system oscillating back and forth with constant total energy.

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