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...