Question

Three identical masses, each with mass ( m ) are connected in a line to each other and to two fixed points by four identical springs of spring constant ( k ). The masses are free to move without friction on the x-axis. If we denote the position of the masses, relative to their equilibrium positions, as ( x_{1}, x_{2} ), and ( x_{3} ) respectively, the differential equations that describe their motion are: [ egin{aligned} m frac{d^{2}}{d t^{2}} x_{1} & =-2 k x_{1}+k x_{2} \ m frac{d^{2}}{d t^{2}} x_{2} & =k x_{1}-2 k x_{2}+k x_{3} \ m frac{d^{2}}{d t^{2}} x_{3} & =k x_{2}-2 k x_{3} end{aligned} ] 8. By subtracting equation 3 from equation 1 above, you can obtain a differential equation which shows that the combination ( x_{1}-x_{3} ) undergoes harmonic motion. If ( k=10 frac{N}{m} ) and ( m=2 mathrm{~kg} ), what is the frequency ( f ) of this oscillation? (a) ( 0.36 H z ) (b) ( * * * 0.50 mathrm{~Hz} ) (c) ( 1.19 mathrm{~Hz} ) (d) ( 2.24 H z ) (e) ( 3.16 H z )

          Three identical masses, each with mass ( m ) are connected in a line to each other and to two fixed points by four identical springs of spring constant ( k ). The masses are free to move without friction on the x-axis. If we denote the position of the masses, relative to their equilibrium positions, as ( x_{1}, x_{2} ), and ( x_{3} ) respectively, the differential equations that describe their motion are:
[
egin{aligned}
m frac{d^{2}}{d t^{2}} x_{1} & =-2 k x_{1}+k x_{2} \
m frac{d^{2}}{d t^{2}} x_{2} & =k x_{1}-2 k x_{2}+k x_{3} \
m frac{d^{2}}{d t^{2}} x_{3} & =k x_{2}-2 k x_{3}
end{aligned}
]
8. By subtracting equation 3 from equation 1 above, you can obtain a differential equation which shows that the combination ( x_{1}-x_{3} ) undergoes harmonic motion. If ( k=10 frac{N}{m} ) and ( m=2 mathrm{~kg} ), what is the frequency ( f ) of this oscillation?
(a) ( 0.36 H z )
(b) ( * * * 0.50 mathrm{~Hz} )
(c) ( 1.19 mathrm{~Hz} )
(d) ( 2.24 H z )
(e) ( 3.16 H z )

$Three identical masses, each with mass ( m ) are connected in a line to each other and to two fixed points by four identical springs of spring constant ( k ). The masses are free to move without friction on the x-axis. If we denote the position of the masses, relative to their equilibrium positions, as ( x1, x2 ), and ( x3 ) respectively, the differential equations that describe their motion are: [ eginaligned m fracd^2d t^2 x1 =-2 k x1+k x2 m fracd^2d t^2 x2 =k x1-2 k x2+k x3 m fracd^2d t^2 x3 =k x2-2 k x3 endaligned ] 8. By subtracting equation 3 from equation 1 above, you can obtain a differential equation which shows that the combination ( x1-x3 ) undergoes harmonic motion. If ( k=10 fracNm ) and ( m=2 mathrm kg ), what is the frequency ( f ) of this oscillation? (a) ( 0.36 H z ) (b) ( * * * 0.50 mathrm Hz ) (c) ( 1.19 mathrm Hz ) (d) ( 2.24 H z ) (e) ( 3.16 H z )$

Added by Mark C.

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