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What information can be inferred from Figure 1, the velocity-versus-time graph of a particle in simple harmonic motion?
From Figure 1, the velocity-versus-time graph of a particle in simple harmonic motion, we can infer the amplitude, period, and phase of the motion. The amplitude is the maximum velocity reached by the particle, the period is the time taken to complete one full cycle of motion, and the phase indicates the starting point of the motion within the cycle.
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What requirement must be satisfied by a force acting on a particle in order for the particle to undergo simple harmonic motion?
The force acting on the particle must be directly proportional and opposite in direction to the displacement from the equilibrium position. This requirement ensures that the particle experiences a restoring force that brings it back towards the equilibrium position, allowing for simple harmonic motion to occur.
How can you tell that a motion is simple harmonic?
A motion is simple harmonic if the acceleration of the particle is proportional to the displacement of the particle from the mean position and the acceleration is always directed towards that mean position.
What characteristics of figure 1, the velocity-versus-time graph of a particle in simple harmonic motion, can provide insights into the behavior of the particle during its oscillation?
The characteristics of the velocity-versus-time graph of a particle in simple harmonic motion can provide insights into the particle's behavior during its oscillation by showing the amplitude, frequency, and phase of the motion. The shape of the graph can indicate whether the motion is smooth and periodic, and the slope at different points can reveal the particle's speed and direction at those times.
How can you show that a particle returns to its position when the wave has passed?
When a wave passes through a particle, the particle oscillates around its equilibrium position. If the wave is a simple harmonic wave, the particle will return to its original position after one complete wave cycle since the restoring force is proportional and opposite to the displacement of the particle. Mathematically, this can be shown by analyzing the equation of motion for the particle.
What is it called when a particle of a medium vibrates back and forth?
When a particle of a medium vibrates back and forth, it is called simple harmonic motion. This type of vibration occurs in a periodic manner around a central equilibrium position.
What is maximum at mean position for particle performing simple harmonic motion?
Velocity is maximum at mean position for particle performing simple harmonic motion. Another feature that is maximum at this position is kinetic energy.
Is motion of swing an example of simple harmonic motion?
A body undergoes simple harmonic motion if the acceleration of the particle is proportional to the displacement of the particle from the mean position and the acceleration is always directed towards that mean. Provided the amplitude is small, a swing is an example of simple harmonic motion.
What requirement must be satisfied by a force acting on a particle in order for the particle to undergo simple harmonic motion?
The force acting on the particle must be directly proportional and opposite in direction to the displacement from the equilibrium position. This requirement ensures that the particle experiences a restoring force that brings it back towards the equilibrium position, allowing for simple harmonic motion to occur.
How can you tell that a motion is simple harmonic?
A motion is simple harmonic if the acceleration of the particle is proportional to the displacement of the particle from the mean position and the acceleration is always directed towards that mean position.
What characteristics of figure 1, the velocity-versus-time graph of a particle in simple harmonic motion, can provide insights into the behavior of the particle during its oscillation?
The characteristics of the velocity-versus-time graph of a particle in simple harmonic motion can provide insights into the particle's behavior during its oscillation by showing the amplitude, frequency, and phase of the motion. The shape of the graph can indicate whether the motion is smooth and periodic, and the slope at different points can reveal the particle's speed and direction at those times.
If a particle undergoes Simple harmonic motion with amplitude 18 m what is the total distance it travels in one period?
72
How can you show that a particle returns to its position when the wave has passed?
When a wave passes through a particle, the particle oscillates around its equilibrium position. If the wave is a simple harmonic wave, the particle will return to its original position after one complete wave cycle since the restoring force is proportional and opposite to the displacement of the particle. Mathematically, this can be shown by analyzing the equation of motion for the particle.
What is it called when a particle of a medium vibrates back and forth?
When a particle of a medium vibrates back and forth, it is called simple harmonic motion. This type of vibration occurs in a periodic manner around a central equilibrium position.
What are the types of circular motion?
1) Pathway of a charged particle when it enters a magnetic field... 2) Pendulum oscillations. (simple harmonic motion)
What is the expectation value of position in the harmonic oscillator system?
In the harmonic oscillator system, the expectation value of position is the average position that a particle is most likely to be found at. It is calculated as the integral of the position probability distribution function multiplied by the position variable.
Is the acceleration of a particle moving with simple harmonic motion inversely proportional to the displacement of the particle from the mean position?
Acceleration is directly proportional to displacement in simple harmonic motion.There are perhaps two good explanations for this, one technical and one intuitive.First let us define simple harmonic motion.When a particle moves in a straight line so that the displacement of the particle with time is exactly given by a simple sine (or cosine) of time, then that it is simple harmonic motion.For example: x=A sine (w t) .Answer 1: (In two steps)(a) If we know position as a function of time, we know velocity is the time rate of change of position.v = w A cosine (w t)(b) If we know velocity as a function of time, we know acceleration is the time rate of change of velocity.a = -w2 A sine (w t)* So, acceleration is proportional to displacement, and a(t)=-w2 x(t).Answer 2: (In three steps)(a) Simple harmonic motion occurs when a mass on an ideal spring oscillates.(b) From Newton's laws, we know that acceleration is directly proportional to force.a=F/m(c) We know the force of an ideal spring is proportional to displacement (F=-kx).* So, acceleration is proportional to displacement, and a(t)= -k/m x(t).(This also tells is that w2 =k/m.)As a result, "acceleration is directly proportional to displacement in simple harmonic motion."
WHAT WILL BE the phase Difference between acceleration and velocity of particle during SHM?
The phase difference between acceleration and velocity of a particle in simple harmonic motion is π/2 radians (or 90 degrees). This means that at any given point in time, the velocity of the particle lags behind its acceleration by a quarter of a cycle.
