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Why is a ball an example of simple harmonic motion?
A ball can exhibit simple harmonic motion when it is acted upon by a restoring force, like gravity or a spring. As the ball moves back and forth along its path, it experiences a restoring force that pulls it back towards its equilibrium position. This results in a repetitive motion that can be described by a sinusoidal function, characteristic of simple harmonic motion.
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 types of motion is noticed in the pendulum of clock and swing?
The pendulum of a clock exhibits simple harmonic motion, where it swings back and forth in a constant rhythm. A swing also exhibits simple harmonic motion as a person sits and moves back and forth, propelled by gravity and their own momentum.
What is the relationship between phase angle and simple harmonic motion?
In simple harmonic motion, the phase angle represents the starting point of the motion within one cycle. It determines the position of the object at a specific time. The phase angle is related to the amplitude and frequency of the motion, influencing how the object moves over time.
Can you say circular motion is a harmonic motion?
Circular motion can be considered a type of periodic motion, where an object moves in a circular path with a constant speed. Harmonic motion, on the other hand, is a specific type of periodic motion where the restoring force is directly proportional to the displacement from equilibrium. While circular motion is periodic, it does not necessarily exhibit the characteristics of harmonic motion.
The maximum distance an object in simple harmonic motion moves from equilibrium is called the?
amplitude
Is a pendulum a wave?
A pendulum moves in simple harmonic motion. If a graph of the pendulum's motion is drawn with respect with respect to time, the graph will be a sine wave. Pure tones are experienced when the eardrum moves in simple harmonic motion. In these cases "wave" refers not to the thing moving, but to the graph representing the movement.
Why is a ball an example of simple harmonic motion?
A ball can exhibit simple harmonic motion when it is acted upon by a restoring force, like gravity or a spring. As the ball moves back and forth along its path, it experiences a restoring force that pulls it back towards its equilibrium position. This results in a repetitive motion that can be described by a sinusoidal function, characteristic of simple harmonic motion.
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 types of motion is noticed in the pendulum of clock and swing?
The pendulum of a clock exhibits simple harmonic motion, where it swings back and forth in a constant rhythm. A swing also exhibits simple harmonic motion as a person sits and moves back and forth, propelled by gravity and their own momentum.
What is the relationship between phase angle and simple harmonic motion?
In simple harmonic motion, the phase angle represents the starting point of the motion within one cycle. It determines the position of the object at a specific time. The phase angle is related to the amplitude and frequency of the motion, influencing how the object moves over time.
Can you say circular motion is a harmonic motion?
Circular motion can be considered a type of periodic motion, where an object moves in a circular path with a constant speed. Harmonic motion, on the other hand, is a specific type of periodic motion where the restoring force is directly proportional to the displacement from equilibrium. While circular motion is periodic, it does not necessarily exhibit the characteristics of harmonic motion.
If a mass is attached to the side of a wheel and the wheel rotates back and forth without energy being lost is this Simple Harmonic Motion?
No. The situation is basically the same as with a simple pendulum. If it only moves back and forth over a small angle, it's a fairly good approximation of simple harmonic motion.
A force that acts on an object does only when the object moves?
A force will produce acceleration when the object moves. force in the line of motion will increase the acceleration and the force opposite to the line of motion will decrease the acceleration.
What is the difference between simple harmonic motion and periodic motion?
A periodic motion is any motion that repeats itself with a fixed period. It can be anything from the motion of a comet around the sun to stamping your foot on the floor. It just has to happen repeatedly and the same motion at the same time intervals. Simple harmonic motion is a very special motion. In the purest form, one only uses this term when the motion can be described a varying sinusoidally, i.e. like a sine or cosine function. The motion then has one frequency and one period. The oscillation of spring with a weight is a good real world approximation to this idealized idea of simple harmonic motion. Staying with the strict terminology one will sometimes allow for harmonic overtones in a motion and use the term, "harmonic motion." In other words, like a guitar string, when plucked it has a basic frequency but may also include multiples of that frequency. Still, it has a fixed period. Usually the language is more relaxed and if something is simple harmonic motion it is sometimes merely called harmonic motion. Conversely, though it is not entirely correct, you will hear it said that a guitar string give a pure tone and exhibits simple harmonic motion when that is not strictly true. So, there is a hierarchy of terminology. If you say something is oscillating, or is oscillatory, you are saying something weak, that it repeats itself on a more or less regular basis. Even things like glacier formation can be said to be oscillatory. If the process is periodic, then you can count on it repeating itself on a precise and regular basis and the time for that repetition is the period. Comets were an earlier example, but the motion of a pendulum is periodic and rotation of the wheel on a car at a constant speed is periodic. All periodic motion is also oscillatory in the sense of repeating in time. (One does not normally call circular motion oscillatory only because it is such a highly specialized form of periodic motion, but technically it is periodic.) Harmonic motion means that the time evolution process is described well by a sinusoidal variation. If it is harmonic, then it is also periodic and oscillatory. It is not common to be so precise as to whether only one frequency of sine wave is needed for harmonic motion or perhaps several multiples of the basic frequency. If it is several, it is harmonic and period and oscillatory but it is not simple harmonic. There is a grey area as to whether one should call some motions harmonic with several frequencies or merely periodic. If it takes more than a few frequencies, then it is usually complicated enough to lose the characterization of harmonic, but it is still periodic. Simple harmonic motion is a pure thing and hence an idealization. A pure pitch of sound may be said to be a simple harmonic motion of the air waves. A pure color of light results from a perfect sinusoidal (and hence simple harmonic) variation of electromagnetic fields. A bouncing weight attached to an ideal spring moves in simple harmonic motion. If it is not a simple sine or cosine description, then it is not simple harmonic. If it is simple harmonic, then it is harmonic and if harmonic, periodic and if periodic, oscillatory. Recognize that careful scientific use of these terms is different than casual use in the general language.
How are motion and acceleration different?
In Simple motion, there is no force being applied. The moving object moves in a straight line with constant velocity. In acceleration, there is a force applied. The object's velocity is changing. The first derivative of acceleration is velocity. The first derivative of velocity is distance. (Derivative is a calculus thing.)
Where is acceleration greatest in circular motion?
If an object moves in a circle at a constant speed, the magnitude of the acceleration won't change.
