Simple question regarding higher frequency vs lower frequency

[Doc Z]

Homework Statement

Damping is negligible for a 0.145 kg object hanging from a light 6.30 N/m spring. A sinusoidal force with an amplitude of 1.70 N drives the system. At what frequency will the force make the object vibrate with an amplitude of 0.440 m?

Homework Equations

I don't know how to put formulas in here but basically find out the initial omega value, then plug it into the forced oscillations amplitude equation to get the angular frequency. Then use the frequency formula to get your frequency.

The Attempt at a Solution

Here's the problem!

The question asks me for 2 solutions -- higher frequency and lower frequency.

I obtained the higher frequency given the equations above and it is indeed the correct answer. That answer is 1.33 Hz.

Now how do I get the lower frequency? It's not -1.33 if anyone is wondering.

Thanks for the help guys!

 

[Redbelly98]

Welcome to PF, Doc Z.

It's been a while since I solved this type of problem. But I remember that the amplitude equation involves frequency terms that are squared.

When you worked through your solution, you probably took a square root at some point. Did you consider the negative square root as well?

 

[Doc Z]

Sorry for the late response, for some reason I didn't get an email when I receive a reply to a thread.

Thank you very much! It was just a stupid mistake on my part, I completely forgot about the negative sign.

 

[Redbelly98]

... for some reason I didn't get an email when I receive a reply to a thread.

Yeah, that happens sometimes. It seems to be a bug in the system.

If you click on "My PF" at the top left of the page, you'll see a list of recent replies in threads you are subscribed to. I have abandoned email notification in favor of this other way of checking for recent replies.

Glad the HW problem worked out.