Longer pendulum, does frequency need to be increased or

[Perseverence]

A motor drives a pendulum at its natural frequency and keeps it swinging at a constant rate. If this motor uses a longer pendulum, does a frequency need to be increased or decreased?

I'm assuming that the question is asking whether or not the frequency that the motor drives a pendulum needs to be increased to maintain the same swing rate. I don't know if they're actually asking for something else and I can't see it.

Frequency seems to be inversely proportional to length. So it seems that as length increases frequency will decrease so therefore to maintain the same frequency as the original length the motor will have to increase the frequency. But that is not the answer that is given for the question.

The answer states that increasing the length of the pendulum necessitates decreasing the frequency of the motor.

What am I missing here? The given answer seems wrong

 

[phinds]

What am I missing here?

Presumably what you are missing is the interpretation of the poorly worded problem statement that implies that the motor is to use the natural frequency of the new length, not force the old frequency onto the new length. That's what "natural frequency" implies but it should have been stated more clearly.

 

[Perseverence]

Holy cow! Thank you so much for the explanation. I was completely flummoxed there for a second. The world makes sense again. Thank you thank you thank you thank you!

 

[phinds]

The world makes sense again.

Oh, give it time. That illusion never lasts

 

[Perseverence]

Oh, give it time. That illusion never lasts

oh wow. So true. And completely flummoxed by a whole new question. I keep working at becoming one with the love of physics, but it's just not happening. The whole process is so painfully frustrating.

Thank goodness for physics forum to keep us from completely walking over the edge into the abyss of unrelenting confusion