Displacement Meter- Simple Harmonic Motion

[dvep]

Homework Statement

The figure attached shows the meter used to study the motion yB = bsinωt.
The motion of the mass relative to the frame is recorded on the drum.
If l1= 360 mm, l2= 480 mm, l3= 600 mm, m = 0.9 kg, c = 1.4 Ns/m and
ω = 10 rad/s, Determine the range of the spring constant k over which the magnitude of the recorded relative displacement is less than 1.5b. It is assumed that the ratio ω/ωn must remain greater than unity

Homework Equations

mx'' +cx' + kx = 0

w = sqrt(k/m)

The Attempt at a Solution

-m(w^2)bsinwt + cwbcoswt + kbsinwt = 0
cb(k/m)coswt = 0

This is what I've done so far, I am quite lost on this question am I at all on the right track?
Should I use the conservation of energy?

 

[dvep]

Any help at all would would be appreciated with this, really stuck.

 

[Quinzio]

the recorded relative displacement is less than 1.5b.

1.5b

What is b ?

ω = 10 rad/s,

What is ω ? Where is it applied ?

 

[dvep]

1.5b

What is b ?



What is ω ? Where is it applied ?

b is the amplitude of the oscillation and \omega is the angular velocity. what do you mean by where is it applied?

 

[Skittles999]

b is the amplitude of the oscillation and \omega is the angular velocity. what do you mean by where is it applied?

\omega is the angular velocity of the rotating drum (see attached image above)

 

[Quinzio]

\omega is the angular velocity of the rotating drum (see attached image above)

Naa, honestly I think the drum is just the equivalent of a modern oscilloscope. No one cares about the drum.
It could well be that ω is the angular velocity of the metal rod, which moves of small angles, but has a ω.

More simply, I think ω is the pulsation of the spring-mass system.

More mysterious is b. If I displace the mass m an then let it free to move, that displacement will be the biggest that will be recorded, because the system will generate a damped series of oscillation with decreasing amplitude.
So, what does it mean to keep the amplitude less than 1.5b ?Ah ok, wait a minute, what is the meaning of the Yb = bsin wt in the right bottom corner ?
It means that the whole system , the box is "shaken" with a movement like b sin wt.

Ok, now things make sense. So you got a forced oscillator, with a sinusoidal force.

You can look here:
http://en.wikipedia.org/wiki/Harmonic_oscillator
section Sinusoidal driving force

 

[Skittles999]

Naa, honestly I think the drum is just the equivalent of a modern oscilloscope. No one cares about the drum.

Sorry, yes you are correct

 

[dvep]

Naa, honestly I think the drum is just the equivalent of a modern oscilloscope. No one cares about the drum.
It could well be that ω is the angular velocity of the metal rod, which moves of small angles, but has a ω.

More simply, I think ω is the pulsation of the spring-mass system.

More mysterious is b. If I displace the mass m an then let it free to move, that displacement will be the biggest that will be recorded, because the system will generate a damped series of oscillation with decreasing amplitude.
So, what does it mean to keep the amplitude less than 1.5b ?


Ah ok, wait a minute, what is the meaning of the Yb = bsin wt in the right bottom corner ?
It means that the whole system , the box is "shaken" with a movement like b sin wt.

Ok, now things make sense. So you got a forced oscillator, with a sinusoidal force.

You can look here:
http://en.wikipedia.org/wiki/Harmonic_oscillator
section Sinusoidal driving force

Thanks for your reply.
I have a fair understanding of it, but still quite confused on how to do this problem and where all the different equations are coming from.
Do I find the steady-state solution and use that to find k?

 

[ercapitano]

any insight on this question?? I have a very similar question and can't seem to figure it out...