When the vibration period is T.T = 0, the particle is in the equilibrium position and the motion direction is in the positive direction of y-axis, and the particle moves to 1 / 2 of the maximum displacement at t, the shortest time required for this distance is calculated

When the vibration period is T.T = 0, the particle is in the equilibrium position and the motion direction is in the positive direction of y-axis, and the particle moves to 1 / 2 of the maximum displacement at t, the shortest time required for this distance is calculated

From the angular frequency of resonant motion: ω = 2 π F, in the question: T = 1 / F, the solution is: ω = 2 π / T
When t = 0, the initial phase angle is equal to zero
So there is a displacement: S = ACOS ω t
When s = A / 2, cos ω t = 1 / 2, then ω t = n π + π / 6
T = (n π + π / 6) t / 2 π, when n = 0, Tmin = t / 12

When a particle moves from the equilibrium position to the positive direction of the x-axis, the time required for the distance from the equilibrium position to half of the maximum displacement is
A fraction of T
Can you be more detailed ~ my foundation is not very good

Arcsin (1 / 2) = π / 6 (π / 6) / (2 π) = 1 / 12, so it needs 12 / 12 t

How to judge the direction of acceleration and velocity in simple harmonic motion?
Can you explain the white point, how to judge the speed?

First, find the balance point. When you vibrate left and right, the acceleration will turn right at the left of the balance point, and turn left at the right of the balance point. The speed direction is seen from the motion; the up and down vibration analogy is good. In the speed direction, the object moves to the left, the speed direction will turn left, the object moves to the right, the speed direction will turn right, and the up and down analogy is good

Acceleration problem of simple harmonic motion
Acceleration and centripetal acceleration in simple harmonic motion of pendulum are confused. I don't know how to distinguish them
And what is the acceleration direction at the equilibrium position of the pendulum?

The acceleration of a simple pendulum is the acceleration of an object in the direction of motion
Centripetal acceleration is the acceleration produced by a rope or other rod to push an object in a direction perpendicular to its direction of motion, causing the object to swing around the center of a circle, extending the direction of the rope or rod
In the equilibrium position, the acceleration direction of the object is vertical upward. Because the force in the horizontal position is balanced, both sides of the motion direction are possible. It depends on the motion direction of the object at the previous moment. In the equilibrium position, its centripetal acceleration is vertical upward

How does the acceleration of simple harmonic motion change? Take o as the equilibrium position, a and B are the maximum displacement

The restoring force of simple harmonic motion is its combined external force, f = - KX, where the negative sign indicates the opposite direction of displacement, so a = f / M = - KX / m

The change law of displacement, restoring force, velocity and acceleration in simple harmonic motion

(1) The displacement X in the vibration starts from the equilibrium position, and its direction points from the equilibrium position to the end position. Its size is the linear distance between the two positions. It is the largest at the two "ends" and zero at the equilibrium position
(2) The change of acceleration is consistent with the change of acceleration, which is the largest at the two "ends", zero at the equilibrium position, and always points to the equilibrium position
(3) The change of velocity and acceleration is just opposite, which is zero at two "ends" and maximum at equilibrium position. Except for two "ends", there are two possible directions of velocity at any position

How does velocity, acceleration and displacement change in simple harmonic motion and where does it point?

In simple harmonic motion, "displacement" refers to the displacement of the relative equilibrium position. When the object moves away from the equilibrium position, the velocity decreases, the acceleration increases, and the displacement increases. The velocity direction is the direction of motion, the acceleration direction points to the equilibrium position, and the displacement direction points to the equilibrium position. When the object moves towards the direction close to the equilibrium position, the velocity increases, the acceleration decreases, and the displacement decreases
Velocity direction is motion direction, acceleration direction points to equilibrium position, displacement direction points to equilibrium position
At the equilibrium position, the velocity is the maximum, the acceleration is 0, and the displacement is 0;
At the two maximum displacements, the velocity is 0, the acceleration is maximum and the displacement is maximum

What are the positive and negative meanings of velocity, displacement and acceleration in physical harmonic motion

The positive sign represents the positive direction and the negative sign represents the opposite direction, regardless of size

The acceleration of point a is 2 meters per second, and the direction of B is 3 meters per second

The acceleration is only related to the direction of the force

What are motion equation, vibration equation, wave equation and wave equation in simple harmonic motion?

Vibration propagates outward, that is, wave,
The vibration equation is the vibration equation of a point, and the wave equation is the vibration equation of any point