pendulum question?

Question

A physics student, bored by a lecture on simple harmonic motion, idly picks up his pencil (mass 9.2g, length 17cm ) by the tip with his frictionless fingers, and allows it to swing back and forth with small amplitude.If the pencil completes 6279 full cycles during the lecture, how long does the lecture last?

I still can't get the right answer.
Can sombody show me how to do this question using simple harmonic motion equation?

Answer 1

I'm only 15 but I think I have an accurate answer. I'm just trying my best.

Well I did a quick experiment and a pencil swings almost four times per second. This means about 2 cycles per second.

The Math:

6279cyc / 2cyc x 1sec = approx. 3139.5sec or 3140sec.

3140sec = 52.3333min (answer by Google)

I think that 52min and 20sec is an appropriate answer for a lecture because classes/periods are about 55min at my high school.

Answer 2

Yeah, we use one all the time, in conjunction with listening to the "inner voice". When I can't feel that warmth and peace inside for a question (because I'm not in tune or can't be objective), I use a pendulum. The trick with using a pendulum is you need to be VERY specific about your questions. For instance, we wanted to find out the sex of our baby. We asked, "Is it a boy?" (No.) "Is it a girl?" (No.) Then I suggested to my husband to ask, "Does it have XX chromosomes?" (No.) "Does it have XY chromosomes?" (Yes.) So, I guess the TRUTH was that the foetus was neither a "boy" or a "girl" but was of non-specific gender with the chromosomal potential to become a boy. Other common problem questions may be... "Should I ...?" This works some of the time, and some of the time it doesn't because in some cases there is a range of "right answers." If you take the first "yes" you get, you might be short-changing yourself. The most important thing with using a pendulum is to think out all the possible solutions and ways of asking the questions in your head, and ask all of them. That way you'll eventually get the best guidance.... ie, use heart AND mind. Also, to be on the safe side it's always a good idea to pray to God or benevolent spirit guides before you ask a question, to ensure that it's angels who are answering you, and not some rogue negative entity. And it's nice to say a prayer of thanks, at the end, too. That should help ensure that your answers are coming from the right spiritual source. God bless you. xo Love MumOf4 Added: I have found that sometimes the angels aren't willing to give a straight answer, because the answer is something we're not yet supposed to know. Also, I once had a pendulum that was energetically damaged, and I found it very hard to use. I have found that the clearer the crystal is, the clearer the answer will be. Some pendulums are excellent, some are just mediocre.

Answer 3

All right, T.VO rules.
The bestest answer I ever saw.



Now lets do it by the book, for the sake of homework submission only.

Moment of inertia of the pencil around its cener of gravity Jo.
Length L.
Mass M.

Moment of inertia around the tip
Jt = Jo + M(L/2)² = Jo + ML²/4

Note that if we take a pencil twice as long, then its
moment of inertia around its center of mass is
Jo x (2M/M) x (2L/L)² = 8Jo.

At the same time moment of inertia of this new
double pencil is twice the moment of inertia of
our original pencil around the tip:
8Jo = 2 (Jo + ML²/4)
6Jo = ML²/2
Jo = ML²/12
Jt = Jo + M(L/2)² = ML²/12 + ML²/4 = ML²/3

Dynamic equation:
Jt d²φ/dt² + Mg (φL/2) = 0
d²φ/dt² + MgL / 2Jt φ = 0

Ω² = MgL / 2Jt = MgL / (2/3 ML²) = 3/2 g/L
Ω = √(3/2 g/L) = 9.30 1/s
T = 6279 x (2π/Ω) = 4242 s = 70 minunutes.

Answer 4

Ti Vo is a smart kid. I'll bet everyone else is trying to use center of mass, equations and all that other stuff.

Answer 5

That's one long lecture.

Answer 6

F=1/T where F is frequency & T the period.

T=2pi*(l/g)^0.5

the period of oscillation is 0.827s

I think: 1 cycle occurs every 0.827s implying 6279 cycles will occur at 5192.73s (0.827*6279)

5192.73s/60 =86.55mins