Calculating Phase Difference in Two-Mass Spring System | Homework Help

[ryandaniels]

Homework Statement

There is a spring with 2 masses with a combined mass of 0.69kg. The vertical oscillation has a frequency of 1.5Hz. The amplitude of the oscillation is 30mm.

Now this spring is attached to a horizontal support rod that can be made to oscillate vertically.

how do i work out the phase difference with the driver (the spring)?

Homework Equations

The Attempt at a Solution

If it oscillates with a frequency of 0.2Hz the amplitude will be less than resonance and there will be forced vibrations. , but how do i work out the phase difference with the driver (the spring)?

 

[mfb]

How are the two masses attached to the spring?

If it oscillates with a frequency of 0.2Hz

Where does the value of 0.2 Hz come from?
There is a formula for the phase difference as function of the two relevant frequencies, but you can also solve the equation of motion to derive it.

 

[ryandaniels]

How are the two masses attached to the spring?Where does the value of 0.2 Hz come from?
There is a formula for the phase difference as function of the two relevant frequencies, but you can also solve the equation of motion to derive it.

total mass = 0.69kg and it asks if the supporting rod was frequency 0.2Hz what would the phase be?

 

[mfb]

total mass = 0.69kg

Yes, but where are those masses? If they are at the same place (at the end of the spring?), where is the point of having two masses?

and it asks if the supporting rod was frequency 0.2Hz what would the phase be?

I don't see the number in the problem statement. Please provide the full problem statement.

 

[ryandaniels]

The 2 questions previously stated:

A spring has a fixed support extends by 40mm when a mass of 0.25 kg is suspended from it work out spring constant - answer - 61.3

Then an additional 0.44k is then placed on the spring and the system is set into vertical oscillation, show that the frequency is 1.5Hz

With both masses still in place, the spring is now suspended from a horizontal support rod that can be made to oscillate vertically, with amplitude 30mm at several frequencies.
Describe fully with reference to phase the motion of the masses suspended from the spring in each case:

The support rod oscillates at frequency of 0.2Hz

The support rot oscillates at frequency 1.5Hz

The support rot oscillates at frequency 10Hz

 

[mfb]

"Describe" - I don't think you have to calculate it (and I don't think you can without damping coefficient).

 

[gneill]

If the problem is seeking a phase difference at steady-state (after the support rod has been vibrating at some fixed frequency for a "long" time), then the problem should be amenable to analysis.

Converting the mechanical problem to an electrical analog it would look something like this:

In this analog, springs become inducatances, masses become capacitances. Velocities are voltages and forces are currents.

In the figure $V_b(t)$ is the support rod velocity (not the displacement), and $V_m(t)$ is the mass velocity. The usual steady-state analysis methods for electric circuits can be applied to obtain the output in terms of the input. Yes it'll be a velocity function and not a displacement, but an integration will take care of that.