The hour and minute hands coincide several times throughout the day

In a single day (24 hours), the hour and minute hands coincide exactly 22 times.

11 2 = 22 times.

1 o'clock, 13:30 (another 5 11 minutes.)

2 o'clock, 2 p.m. 60 p.m. (10 11 p.m.)

3 o'clock, 15 o'clock 90 ) and 4 11 minutes.

4 o'clock, 16 o'clock 120 (again 9 11 minutes.)

5 o'clock, 17 o'clock 150 (again 3 11 minutes.)

6 o'clock, 18 o'clock 180 (again 8 11 minutes.)

7 o'clock, 7 p.m. 210 (again 2 11 minutes.)

8 o'clock, 20 o'clock 240 (again 7 11 minutes.)

9 o'clock, 21 o'clock 270 (again 1 11 minutes.

10 o'clock, 22 o'clock 300 (again 6 11 minutes.)

12 o'clock and 24 o'clock.

<> the hour and minute hands coincide 22 times a day.

Assuming that the angular velocity of the hour hand is (6 per hour), the angular velocity of the minute hand is 12 and that of the second hand is 720. The time when the minute hand coincides with the hour hand again is t, then there is 12 t- t=2 , n=22. So, the hour and minute hands coincide 22 times a day.

Regardless of the time of day, the hour and minute hands coincide once an hour. 24 hours a day, which means they coincide 24 times a day.

The angular velocity of the hour hand is w hour hand = 2 12 60 = 360 (rad min), w minute hand = 2 60 = 30 (rad min), so ( 30 360) t = n 2 , where n is equal to the number of coincidences, t is equal to the minute rotation time, and the desired 720n 11 = 1440, the solution n is equal to 22 times. So up to 22 times. I wonder if the analysis is clear?

From 00:00:00 to 24:00:00, the hour hand coincides with the minute hand 23 times.

Among them, 0 o'clock, 12 o'clock, and 24 o'clock coincide on the hour, and 11 o'clock and 23 o'clock do not coincide, and the rest of the o'clock coincides. 10×2+3=23

In total, there are 44 right angles, and the reasons are as follows:

Since the hour hand rotates 30° in one hour, it rotates in 1 minute, and the minute hand rotates 6° per minute. Let the hour hand be at right angle to the minute hand after x minutes, then there is the equation x(6°. If there are n times, then n=88 is solved.

In these 88 times, the hour and minute hands are angled at 90°, 180°, 270°, and 360° respectively, of which 180° and 360° are not satisfactory, so there are a total of 44 right angles.

Quartz Clock Principle:

The core of the quartz crystal sensor is the sensing element - piezoelectric quartz wafer. Its working principle is the piezoelectric effect, that is, after the quartz crystal is subjected to mechanical stress in certain directions, it will produce an electric dipole, on the contrary, if a voltage is applied in a certain direction of quartz, it will be deformed in a specific direction, this phenomenon is called the inverse piezoelectric effect.

If an alternating electric field is applied to the crystal, the crystal lattice will produce mechanical vibrations, and when the frequency of the applied electric field coincides with the natural oscillation frequency of the crystal, the crystal resonance will occur. Due to the low electric field strength produced by quartz crystals under pressure, only a weak applied electric field is required to produce deformation, which makes piezoelectric quartz crystals easily resonate under the excitation of an alternating electric field.

Its oscillation energy loss is small, and the oscillation frequency is extremely stable. This, combined with quartz's excellent mechanical, electrical and chemical stability, has made it a frequency reference component for quartz clocks, electronic watches, televisions, computers, and other digital circuits since the 40s.

An interesting property of quartz crystals is that when a positive current is introduced on one side and a negative current is introduced on the other side, the negative current side retracts and bends into a U-shape.

If positive and negative currents are introduced alternately on both sides of the quartz crystal, the quartz crystal will oscillate. Quartz crystals are timed according to this oscillation. The quartz crystal built into the PC oscillates 14,318,180 times per second. That's how quartz clocks work.

Kick slide 12; 3:17；4:22；5:

Calculation method: every 12 hours, the hour hand rotates once, and the minute hand turns 12 times, that is, the minute hand catches up with the hour hand 11 times, so the side source takes 0:00 as the starting point, and the clock can be divided into 11 equal parts in the first half of the day; The time for each side laugh scale is n:

60n/11】。[Indicates an integer.] 0≤n≤10。

In the afternoon, it is recorded once at a certain time in the afternoon, and the time is recorded in the 24-hour method, and 12 hours are added. Extended Information:Knowledge Preparation:

1) Ordinary clocks and watches are equivalent to circles, and their hour or minute hands are equivalent to walking around a 360° angle; (2) The angle corresponding to each large grid on the clock (one hour of the hour hand or 5 minutes of the minute hand) is: 360 12 = 30 ° (3) The angle corresponding to the hour hand movement for every 1 minute should be: 360 (12 60) = minute hand for every 1 minute [

In the 24 hours of the day, the hour hand and the minute hand and the second of the clock form a total of 24 flat angles and 22 circumferential angles.

The flat angle is 1 time per hour, so it is 24 times.

The circumference angle is the number of coincidences, a total of 22 times, and the times are as follows:

1 o'clock, 13:30 (another 5 11 minutes.)

2 o'clock, 2 p.m. 60 p.m. (10 11 p.m.)

3 o'clock, 15 o'clock 90 ) and 4 11 minutes.

4 o'clock, 16 o'clock 120 (again 9 11 minutes.)

5 o'clock, 17 o'clock 150 (again 3 11 minutes.)

6 o'clock, 18 o'clock 180 (again 8 11 minutes.)

7 o'clock, 7 p.m. 210 (again 2 11 minutes.)

8 o'clock, 20 o'clock 240 (again 7 11 minutes.)

9 o'clock, 21 o'clock 270 (again 1 11 minutes.

10 o'clock, 22 o'clock 300 (again 6 11 minutes.)

12 o'clock and 24 o'clock.

Assuming that the angular velocity of the hour hand is (6 per hour), the angular velocity of the minute hand is 12 and that of the second hand is 720. The time when the minute hand coincides with the hour hand again is t, then there is 12 t- t = 2 n

Hours, minutes, seconds.

w 12w 720w

0≤t≤24

12wt-wt=2π*n(n=0,1,2,..12w*n11wt=12w*n

11t=12n

t=12n/11(n=0,1,2,..

t=12*0=0 ,n=0

t=12*1/11=1+1/11 ,n=1t=12*2/11 ,n=2

t=12*3/11 ,n=3

t=12*10/11 ,n=10

t=12*11/11=12 ,n=11

t=12*12/11 ,n=12

t=12*22 11=24, n=22 (the hour and minute hands coincide 22 times a day.) From above, it can be seen that the hour and minute hands coincide 22 times a day; Since 0:00 to 12 o'clock and 12 o'clock to 24 o'clock are symmetrical, it is only necessary to consider whether the hour and minute hands from 0:00 to 12 o'clock coincide and whether the second hand also coincides.

t = 12 11 hours, converted to hours, minutes and seconds is 1 hour and 5 minutes and seconds, obviously the second hand does not coincide with the hour hand and minute hand, and it can also be calculated that the other 10 minutes and minutes coincide with the hour hand, and the second hand cannot coincide with them. It will only coincide when it is positive 12 and 0. So there are only two triple-stitches in a day, at 0 o'clock and 12 o'clock.

Since the angle of the center of the circle rotated by the hour hand for 1 minute is degrees, and the angle of the center of the circle rotated by the minute hand for 1 minute is 6 degrees, when the two needles coincide for the first time and then coincide for the second time, the number of angles of the center of the circle rotated by the minute hand more than the hour hand is 360 degrees, so the time required for the two needles to coincide again is:

t=65+5 11 minutes, this kind of problem is actually a chasing problem of the minute hand chasing the hour hand, and its formula is:

t= s (v1-v2), s=60 (d), minute speed: v1=1 d/min, hour hand speed: v2= 1 12 d/min, so, t=65+5 11 minutes, according to the above calculation, the hour hand and minute hand coincide every 65+5 11 minutes.

That is, from 12 o'clock, every 65+5 11 minutes, the hour hand coincides with the minute hand once, and the whole day coincides 22 times. There are 24 60 = 1,440 (minutes) in one day and night, so two needles coincide 22 times in one day and night.

The number of coincidences = 1440 (65 + 5 11) = 22 times, respectively: 1 hour, 13 hours 30 (again 5 11 points.

2 o'clock, 2 p.m. 60 p.m. (10 11 p.m.)

3 o'clock, 15 o'clock 90 ) and 4 11 minutes.

4 o'clock, 16 o'clock 120 (again 9 11 minutes.)

5 o'clock, 17 o'clock 150 (again 3 11 minutes.)

6 o'clock, 18 o'clock 180 (again 8 11 minutes.)

7 o'clock, 7 p.m. 210 (again 2 11 minutes.)

8 o'clock, 20 o'clock 240 (again 7 11 minutes.)

9 o'clock, 21 o'clock 270 (again 1 11 minutes.

10 o'clock, 22 o'clock 300 (again 6 11 minutes.)

12 o'clock and 24 o'clock.