WOLFRAM|DEMONSTRATIONS PROJECT

Longitudinal Oscillations and Resonance of a Four-Spring, Three-Mass System

​
mass m (kg)
1
spring strength (N/m)
5
damping coeff. (kg/s)
0
frequency ​
-1
s
​
1.71141
initial conditions
x
10
(m)
0
x
20
(m)
0
x
30
(m)
0
v
10
(m/s)
0
v
20
(m/s)
0
v
30
(m/s)
0
show velocities
start/stop/reset
time (sec): 0
Study the longitudinal oscillations and forced vibrations of this system with three degrees of freedom. You can set the initial conditions and the spring strength, damping coefficients, etc.
You can view the free vibrations by setting the frequency of the exciting force to 0. By setting the frequency to one of the resonance frequency values displayed, you can see that resonance. There are three different resonance frequencies, corresponding to the different oscillation modes.
The
x
10
slider changes the elongation of the first mass (masses are the red dots), which is the leftmost one. The
x
20
is for the second, which is the middle one, and
x
30
is for the rightmost mass.
All three bodies have the same mass and they can be changed with the first slider.
The external force "shakes" the right end of the fourth spring with a constant frequency, while the left end of the first spring is fixed.
This frequency can be set with the third slider.
If this frequency is set to 0 then the system performs free vibrations.
The units of the longitudinal elongations are meters.