How to calculate the force on a simple harmonic vibrating body
the restoring force in a simple penlum is a component of gravity; The movement of spring is the pulling force of spring; And electromagnetic force can be used as restoring force...
the most important point is:
F = - KX, satisfying this is restoring force
you don't have a clear idea
where k is the proportional coefficient of the restoring force and displacement, which can not be confused with the stiffness coefficient of the spring; The minus sign means that the direction of the restoring force is always opposite to the direction of the displacement of the object
according to Newton's second law, f = ma, when the mass of the object is fixed, the acceleration of the moving object is always proportional to the magnitude of the resultant force on the object, and the direction of the resultant force is the same. The mechanical energy conservation of simple harmonic motion system.
Displacement of simple harmonic motion x = RCOs ω t+ φ
Velocity V of simple harmonic motion=- ω Rsin ω t+ φ Acceleration a ofharmonic motion=- ω 2Rcos ω t+ φ， The above three equations are the equations of simple harmonic motion
the characteristics of simple harmonic motion
1. The motion route of an object is not necessarily straight line
for example, the motion route of a simple penlum in simple harmonic motion is an arc on both sides of the penlum's equilibrium position and passing through the equilibrium position, that is, the motion route of the penlum is a curve
The displacement of simple harmonic motion refers to the displacement of the vibrating body from the equilibrium position, and the starting point of displacement is always in the equilibrium position. When the body is far away from the equilibrium position, the displacement direction is the same as the velocity direction, and when it is close to the equilibrium position, the displacement direction is opposite to the velocity direction (3) the direction of the restoring force on the vibrating object is not necessarily the same as that of the resultant force on the object.
for example, the swing of a simple penlum near the equilibrium position (within a small angle range) makes both circular motion and simple harmonic motion, and the resultant force of each force on the penlum ball should provide both centripetal force and restoring force for circular motion, That is to say, in the process of simple penlum vibration, one component of the resultant force of all forces on the penlum ball provides centripetal force, and the other component provides restoring force. Then the direction of the restoring force is different from that of the resultant force of the forces on the penlum
For example, when a simple penlum ball moves harmoniously through the balance position, because the balance position of the penlum ball is on the circular arc, and the circular motion of the penlum ball on the circular arc requires centripetal force, the tension of the hanging rope of the penlum ball at the balance position is greater than the gravity of the penlum ball, that is, the penlum ball is not in the balance position| KX < / td > < / TR > < tr > < td > m < / td > < / TR > < / Table >, displacement direction, equilibrium position< Br > maximum, zero, zero, maximum
8. The answer is that Ka
note that the concept of restoring force is proportional to the displacement of the object relative to the equilibrium position, and the direction always points to the equilibrium position. When the object is at the highest point, the force in the direction of downward and in direct proportion to the displacement away from the equilibrium position is the restoring force. The restoring force here is the resultant force on the object Ka is not the spring force. When the object is in the equilibrium position, the spring force is mg, the resultant force is 0, and the restoring force is 0. Now at the highest point, the variable of spring expansion is a, that is, the spring force is mg Ka, or - (KA mg), the direction is not necessarily, and the size is | mg Ka |. And then the resultant force on the object is Ka, which is the restoring force when calculating the restoring force of simple harmonic vibration, it is usually the resultant force of the oscillator. The formula of spring force is f = KX, but it can't be used indiscriminately. Here we don't know what the type variable X of spring is. A is the amplitude, not the type variable, but the change of the type variable. 9.
1. According to the definition, simple harmonic motion is the most basic and simplest mechanical vibration. When a body moves harmoniously, the force on the body is proportional to the displacement and always points to the equilibrium position it is a periodic motion determined by the nature of its own system In fact, simple harmonic vibration is sinusoidal vibration. Therefore, in wireless electricity, a simple harmonic signal is actually a sinusoidal signal It can also be proved by some conditions of simple harmonic motion that the relationship between force and displacement of a body satisfies the following conditions: F = - KX is simple harmonic motion At time t, the displacement x = RCOs ω t+ φ)， Velocity V of simple harmonic motion=- ω Rsin( ω t+ φ)， Acceleration a of simple harmonic motion=- ω^ 2)Rcos( ω t+ φ)， Any one of the three can show that the object is in harmonic motion extended data: derivation of motion equation: the motion of an object in uniform circular motion projected on a diameter is simple harmonic motion: If: R is recorded as the radius of uniform circular motion, that is, the amplitude of simple harmonic motion will ω It is recorded as the angular velocity of uniform circular motion, that is, the circular frequency of simple harmonic motion
will φ When t = 0, the angle of the object in uniform circular motion deviates from the diameter (counterclockwise is the positive direction), that is, the initial phase of simple harmonic motion Then, at t time:the displacement of simple harmonic motion x = RCOs ω t+ φ Velocity V of simple harmonic motion=- ω Rsin ω t+ φ Acceleration a ofharmonic motion=- ω 2Rcos ω t+ φ， The above three equations are the equations of simple harmonic motion Hot content
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