What is the period formula of the pendulum, what is the period formula of the single pendulum?

The period of the single pendulum is:

With the help of simple harmonic movement.

The periodic formula t=2 (m k) and, obviously, the proportional constant.

k is equivalent to mg l in the simple harmonic motion of a single pendulum, and bringing it in, we get the periodic formula t=2 (l g) of a single pendulum. It can be seen that the period of a pendulum is accelerated by the gravitational force at that point.

And the length of the pendulum is determined, which is a very useful formula, so much so from Galileo.

Beginning, the pendulum clock that used it to keep time is still flourishing today.

In the case of small angles, due to the sine value of .

Approximately equal to chord length.

The ratio to the length of the pendulum, so the resulting formula for the period of a single pendulum is always an approximation, and in fact, what physicists have to do is not to measure the world accurately, but to explain it with an ingenious physical model.

In addition, this "small-angle approximation" is a method often used in physics, especially in engineering, although the period of the real pendulum will be slightly larger, but in the case of small angles, compared with the measurement error of gravitational acceleration and pendulum length in experimental operation, it is quite good.

Let the mass of the pendulum ball be m, the length of the rope be l, and the angle between the rope and the vertical direction is represented by . Then the magnitude of the restoring force is mgsin, and the displacement from the translational position x=l, when the swing angle is small, sin is ma=mgsin, mx"=mgsinθ≈mgθ x"=gx l Solving the differential equation gives x=asin(2 (l g) + 0) so there is t=2 (l g).

What is the periodic formula for a single pendulum.

The oscillation period, the time it takes for a free-drooping object to swing backwards. Galileo discovered that the time to complete a swing (i.e., the swing period) is the same regardless of whether the amplitude of the swing is larger or smaller.

When the famous physicist Galileo Galilei was studying at the University of Pisa, his first important scientific discovery of the law of oscillation. At one point he noticed that the chandelier on the church was constantly swinging because of the wind. Although the chandelier swings less and less, each swing seems to be equal in time.

Through further observation, Galileo found that the time to complete an oscillation (i.e., the oscillation period) is the same regardless of whether the amplitude of the oscillation is larger or smaller. This is called the "principle of isochronism of pendulums" in physics. All kinds of mechanical pendulum clocks are made according to this principle.

Later, Galileo experimented with iron of different qualities tied to the end of the rope as a pendulum. He found that as long as the same pendulum rope was used, the swing period did not depend on the mass of the pendulum. Subsequently, Galileo experimented with the same pendulum and with different rope lengths, and finally came to the conclusion:

The longer the pendulum rope, the longer it takes to swing back and forth once (i.e., the swing period).

It's the time it takes to make a round trip.

The formula for a single pendulum is t=2 (l g), where l is the pendulum length and g is the local gravitational acceleration.

Single pendulum is a device that can produce reciprocating swing, one end of the non-heavy thin rod or non-extendable fine mu rope is suspended at a certain point in the gravity field, and the other end is consolidated with a heavy ball, which constitutes a single pendulum.

If the ball is confined to the straight plane of lead, it is a flat pendulum, and if the ball swing is not limited to the straight plane of lead, it is a spherical single pendulum.

Specify:

One of the particle vibration systems is the simplest pendulum, and the objects that swing back and forth around a hanging point are called pendulums, but their periods are generally related to the distribution of the shape, size and density of the object.

However, if the small size of the mass is suspended on a thin rope with a fixed length of l at one end and cannot be extended, the mass is pulled away from the equilibrium position, so that the angle between the string and the plumb line through the suspension point is less than 10°, and the mass reciprocating vibration after letting go can be regarded as the vibration of the particle.

Its period t is only related to the length l and the local gravitational acceleration g, that is, t has nothing to do with the mass, shape and amplitude of the mass, and its motion state can be expressed by the simple harmonic vibration formula.

If the angle of the vibration is greater than 10°, the period of the vibration will increase with the increase of the amplitude, and it will quickly become a single pendulum. If the size of the pendulum ball is quite large, the quality of the rope cannot be ignored, and it becomes a compound pendulum, and the period is related to the size of the pendulum.

The periodic formula for a single pendulum is t=2 (l g), where l is the pendulum length and g is the acceleration due to gravity.

stands for the root number; The single pendulum does a simple harmonic movement.

The period is the square root of the pendulum length.

is directly proportional, inversely proportional to the square root of gravitational acceleration, and has nothing to do with the amplitude and the mass of the pendulum.

The length is much larger than the diameter of the ball, and such a device is called a single pendulum.

2. The conditions for a single pendulum to do simple harmony: in the case of a small pendulum angle (10°), the recovery force of the single pendulum is proportional to the displacement and the direction is opposite, and the single pendulum does simple harmonic motion.

3. The periodic formula of a single pendulum: the period of a single pendulum is proportional to the square root of the pendulum length, inversely proportional to the square root of gravitational acceleration, and has nothing to do with the amplitude and the mass of the pendulum.

5. The single pendulum is subject to gravity and tension, and when the single pendulum is stationary, the gravity and tension of the pendulum ball are balanced.

6. When the single pendulum is pulled away from the equilibrium position and released, the gravity of the pendulum ball and the tension of the line selection are not balanced.

7. The component of gravity along the direction of motion is the recovery force of the mechanical vibration of the pendulum ball.

t=2π√（l/g）。

Let the mass of the pendulum ball be m, the length of the rope be l, and the angle between the rope and the vertical direction is represented by . Then the magnitude of the restoring force is mgsin, and the displacement from the translation position x=l, when the swing angle is very small, sin is ma=mgsin, mx =mgsin mg x = gx l solves the differential equation to obtain x=asin(2 (l g) + 0) so there is t = 2 (l g).

Under the condition that the declination angle is less than 10°, the single pendulum moves.

The approximate period formula is: t=2 (l g). where l is the pendulum length and g is the local gravitational acceleration.

The period of the single pendulum is independent of the amplitude and the mass of the pendulum From the perspective of force, the recovery force of the single pendulum is the tangent of gravity along the arc.

The greater the declination angle, the greater the recovery force, the greater the acceleration, and the greater the arc length in the same time.

Under the condition that the declination angle is less than 10°, the approximate periodic formula for the single pendulum motion is: t=2 (l g). where l is the pendulum length and g is the local gravitational acceleration.

The period of the single pendulum has nothing to do with the amplitude and the mass of the pendulum From the perspective of force, the recovery force of the single pendulum is the component of gravity along the tangent direction of the arc and pointing to the equilibrium position, the larger the declination angle, the greater the recovery force, the greater the acceleration, and the greater the arc length traveled in the same time, so the period has nothing to do with the amplitude and mass, but only related to the pendulum length l and the gravitational acceleration g.

t=2π√(l/g)

It is only related to the pendulum length and the local gravitational acceleration, which is directly proportional to the square root of the pendulum length and inversely proportional to the square root of the local gravitational acceleration.

This formula t=2 (l g) is based on the periodic formula t=2 (m k) of the spring oscillator

It is derived, because the proportion coefficient of a single pendulum in simple harmonic motion (k) k=mg l is substituted into t=2 (m k) to obtain t=2 (l g)

Proof: The swing trajectory of the pendulum ball is an arc. Let the swing angle (the angle at which the pendulum deviates from the vertical direction) be , then the gravity mg of the pendulum ball along the tangent direction of this arc is mgsin

Let the displacement of the pendulum ball from the equilibrium position be x and the pendulum length be l, then when the swing angle is very small, it can be considered that sin = x lSo, the restoring force of a single pendulum is f=-mgx l.

For the system, m, g, and l are all fixed values, so it can be considered that k=mg l, then f=-kx

Therefore, in the case that the single pendulum is very small, the single pendulum does simple harmonic motion.

Substituting k=mg l into = (k m) gives = (g l).The formula for the pendulum period can be obtained from t=2.

t=2π√(l/g).

Hope it helps!

The specific calculation process is as follows:

First of all, you know the cycle formula, right? It's very troublesome for me to enter the root number, so I'll omit it here, and then the key is that the period formula is l=l1 + pendulum diameter d=l2 + pendulum diameter d

d = (t1 square·g 4 squared)-l1=(t2 square·g 4 squared) then (t1 square·g-t2 square·g) 4 square = l1-l2 then g = (l1-l2)·4 square (t1 square - t2 squared) This is the formula for acceleration.

The periodic formula for a single pendulum is t=2 (l g).

The formula t=2 l g is derived from the periodic formula t=2 m k of the spring oscillator, because the proportional coefficient of a single pendulum in simple harmonic motion (k in f=-kx) k=mg l is substituted into t=2 m k to obtain t=2 l g.

The periodic formula for a single pendulum is t=2 (l g). The formula t=2 l g is derived from the periodic formula t=2 m k of the spring oscillator, because the proportional coefficient of a single pendulum in simple harmonic motion (k in f=-kx) k=mg l is substituted into t=2 and m k is substituted to obtain t=2 l g.

Formula for the travel cycle of a single pendulum:

is t=2 (l g), which is only related to the pendulum length and the local gravitational acceleration, which is directly proportional to the square root of the pendulum length and inversely proportional to the square root of the local gravitational acceleration.

The formula t=2 l g is derived from the periodic formula t=2 m k of the spring oscillator, because the proportional coefficient of a single pendulum in simple harmonic motion (k in f=-kx) k=mg l is substituted into t=2 m k to obtain t=2 l g. Proof: The swing trajectory of the pendulum ball is an arc.

Let the swing angle (the angle at which the pendulum ball deviates from the vertical direction) be , then the gravity mg of the pendulum ball along the tangent direction of this arc is mgsin Let the displacement of the pendulum ball from the equilibrium position be x and the pendulum length is l, then the pendulum angle is very small.

It can be considered sin x lSo, the restoring force of a single pendulum is f=-mgx l.For the system, m, g, and l are all fixed values, so it can be considered that the file judgment beam k=mg l, then f=-kx

Therefore, in the case that the single pendulum is very small, the single pendulum does simple harmonic motion.

1. The periodic formula of a single pendulum is t=2 (l g). 2. Prove: the swing trajectory of the pendulum ball is a cavity arc, and the swing angle (the angle at which the pendulum ball deviates from the vertical direction) is , then the gravity mg of the pendulum ball is mgsin along the tangent direction of the arc, and the displacement of the pendulum ball from the equilibrium position is x and the pendulum length is l, then when the swing angle is very small, it can be considered that sin = x l.

Therefore, the recovery force of a single pendulum is f=-mgx For the system, m, g, and l are all fixed suffocation car values, so it can be considered that k=mg l, then f=-kx. Therefore, in the case of a very small single pendulum, the hand accompanies the single pendulum to do simple harmonic movement.