Answer :
I think you're trying to take the formulas for speed, wavelength, and
frequency of a wave, and apply them to a pendulum. You can't do that.
It doesn't work.
A pendulum is moving in 'simple harmonic motion', not wave motion.
It's speed is continuously changing, from zero at both ends of its swing,
to maximum as it passes through the 'rest' position at the bottom. And
there's no wavelength defined for a pendulum ... if you're thinking that
it could be the distance from end to end of its swing, or maybe half of
that, you should know that the frequency of an ideal simple pendulum
is not related to that distance at all.
Finally, in the real world, the numbers in this question really kind of
don't make any sense. You have a structure where some part of it is
roughly a foot long (0.35m = 13.8 inches), and at least at some point
during its swing, something is moving at 30 m/s ... about 67 mph !
If something like that could even stay on the table, and IF its frequency
were (speed/wavelength) ... like a wave's frequency is ... then its frequency
would be (30 / 0.35) = 85.7 Hz ! ! The thing would be wiggling back and
forth every 0.017 second ! It would need to be operated only inside
a bomb shelter, with all personnel withdrawn beyond a safe perimeter
before it flies apart and scatters shrapnel everywhere.
We know that there is a formula velocity = frequency x wavelength for all types of waves.
If we assume one complete oscillation of a pendulum to be wavelength we can apply the above formula for the pendulum too.
So as v = fλ and f = v/λ we can just plug in the values to get our answer of frequency.
So frequency = 30/0.35 which is equal to 85.17 Hertz (Hz).
