Oscillation of two masses connected to springs and a fixed point


by haleyae
Tags: connected, fixed, masses, oscillation, point, springs
haleyae
haleyae is offline
#1
Apr26-12, 01:35 AM
P: 1
Q: Two masses m are connected by identical springs of constants k and they lie on a perfectly smooth surface. The extremity of one spring is fixed on the wall, the other one is loose.

Find the equations for the motion of the system.
Find the frequencies of oscillations.

1. Relevant equations:

F=
m[itex]\frac{(d2x)}/{(dt2)}[/itex]

F=kx

2. Attempt:

Part 1:
m[itex]\frac{d2x}{dt2}[/itex] = k(x2-x1)-kx1

m[itex]\frac{d2x}{dt2}[/itex] = k(x1-x2)-kx2

Part 2:

x1=A1cosωt
x2=A2cosωt

and then substitute?


Not sure if I even am getting anywhere with this..
Attached Thumbnails
Untitled.png  
Phys.Org News Partner Physics news on Phys.org
Physicists design quantum switches which can be activated by single photons
'Dressed' laser aimed at clouds may be key to inducing rain, lightning
Higher-order nonlinear optical processes observed using the SACLA X-ray free-electron laser
mikeph
mikeph is offline
#2
Apr26-12, 03:04 AM
P: 1,200
from looking at it there are two modes, one strech mode (both moving in same direction) and one anti-strech (moving in opposite directions), from memory of dynamics class a long time ago you might want to try some substitutions, which reflect these anticipated modes, in the general equation.

For example, the stretch mode looks as if x2 will move with twice the amplitude of x1, so you could guess a solution X = x1 + 2x2, and sub this in to see if it reduces to a SHM equation in X only. I can't see your equations and I don't have any pen or paper so I can't test this idea. Someone else will hopefully confirm it.
sambristol
sambristol is offline
#3
Apr26-12, 05:46 AM
P: 84
your second differential equation in 'part 1' is wrong - the only force acting on the mass is the single spring attached to the end mass.

The general solution is got by adding and subtracting the two differential equations and then expressing them in terms of the 'normal variables' which are q1=x2-x1 and q2 =x1+x2

Solve in terms of these and you can work back to the original variables.


Register to reply

Related Discussions
Oscillation of a point x in [c, d] <N => oscillation of subintervals of partition <N Topology and Analysis 6
Mass connected to two springs Introductory Physics Homework 4
Harmonic Oscillation of two point masses Advanced Physics Homework 2
Oscillation with Two Springs (SMH) Introductory Physics Homework 5
Normal coordinates and frequencies of four masses connected by springs on a circle Advanced Physics Homework 2