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When are the displacement velocity and acceleration equal to zero for the motion of a mass on a spring?
Wiki User
∙ 10y ago
Displacement and acceleration are zero at the instant the mass passes through
its "rest" position ... the place where it sits motionless when it's not bouncing.
Velocity is zero at the extremes of the bounce ... where the expansion and compression
of the spring are maximum, and the mass reverses its direction of motion.
Wiki User
∙ 10y ago
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Define simple harmonic motion . prove that vibrating motion of mass attached to spring is Simple harmonic motion?
its is the motion in which acceleration is directly proportion to the displacement from a fix point and always directed towards the center
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."
Why is displacement directly proportional to acceleration?
Acceleration is given by the equation v-u/t, whereby v is the final velocity of a body, u is the initial velocity and t is the time. So for there to be acceleration, there has to be a change in initial velocity (the starting speed of the body) and the final velocity of the body or if there is no change it would be 0/t and hence the acceleration will be 0. And we know that with a change in speed there has to be a change in displacement i.e. s=d/t. So to sum all this up with an increase in acceleration there is an increase in distance. But this is a very tricky question because you asked about displacement and since displacement is a vector quantity, it has both magnitude and direction. So if a body accelerates forward, then its acceleration is directly proportional to its displacement. However, if the body stops and starts accelerating backwards, it becomes a whole new different story. Given that displacement has direction, if the body moves backwards, then the displacement will be negative, but the acceleration positive. So displacement is directly proportional to acceleration ONLY when a body is moving forwards, but displacement is indirectly proportional to acceleration when a body is moving backwards from it's point of rest. But for distance, given that it is a scalar quantity, it only has magnitude so it is not affected by the direction of movement of the body. So distance is directly proportional to acceleration when a body is moving both forwards and backwards.
What is the relationship between displacement and time?
There is no direct relationship between the two. Newton's Second Law, though, tells you how the VELOCITY of an object will change when a force is applied. The law - as it is usually quoted - says:F = ma Solving for acceleration: a = F/m So, the acceleration of an object will depend on the force. If you integrate this equation twice, you get the displacement - but the integration will also give you two arbitrary integration constants, meaning that you need to know the initial conditions (initial position, and initial velocity).
What are the characteristics of simple harmonic motion?
The characteristics of simple harmonic motion are undamped, undriven, periodic motion. Any equation of motion that can be derived through the use of the following restoring force: F = -kx, where F is the force vector, k is the spring constant, and x is displacement vector, will exhibit simple harmonic motion. The motion itself is described by the equation x(t) = Acos(wt + p), where x(t) is the position as a function of time, A is the amplitude of the motion, w is its angular frequency, and p is the phase.
Define simple harmonic motion . prove that vibrating motion of mass attached to spring is Simple harmonic motion?
its is the motion in which acceleration is directly proportion to the displacement from a fix point and always directed towards the center
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."
Why is displacement directly proportional to acceleration?
Acceleration is given by the equation v-u/t, whereby v is the final velocity of a body, u is the initial velocity and t is the time. So for there to be acceleration, there has to be a change in initial velocity (the starting speed of the body) and the final velocity of the body or if there is no change it would be 0/t and hence the acceleration will be 0. And we know that with a change in speed there has to be a change in displacement i.e. s=d/t. So to sum all this up with an increase in acceleration there is an increase in distance. But this is a very tricky question because you asked about displacement and since displacement is a vector quantity, it has both magnitude and direction. So if a body accelerates forward, then its acceleration is directly proportional to its displacement. However, if the body stops and starts accelerating backwards, it becomes a whole new different story. Given that displacement has direction, if the body moves backwards, then the displacement will be negative, but the acceleration positive. So displacement is directly proportional to acceleration ONLY when a body is moving forwards, but displacement is indirectly proportional to acceleration when a body is moving backwards from it's point of rest. But for distance, given that it is a scalar quantity, it only has magnitude so it is not affected by the direction of movement of the body. So distance is directly proportional to acceleration when a body is moving both forwards and backwards.
What is the relationship between displacement and time?
There is no direct relationship between the two. Newton's Second Law, though, tells you how the VELOCITY of an object will change when a force is applied. The law - as it is usually quoted - says:F = ma Solving for acceleration: a = F/m So, the acceleration of an object will depend on the force. If you integrate this equation twice, you get the displacement - but the integration will also give you two arbitrary integration constants, meaning that you need to know the initial conditions (initial position, and initial velocity).
What are the characteristics of simple harmonic motion?
The characteristics of simple harmonic motion are undamped, undriven, periodic motion. Any equation of motion that can be derived through the use of the following restoring force: F = -kx, where F is the force vector, k is the spring constant, and x is displacement vector, will exhibit simple harmonic motion. The motion itself is described by the equation x(t) = Acos(wt + p), where x(t) is the position as a function of time, A is the amplitude of the motion, w is its angular frequency, and p is the phase.
How does a pogo stick bounce?
your Fnet forces the pogo stick down on the spring because Fnet=ma Mass and acceleration, your acceleration is that of gravity (9.8m/s/s) so you can force the spring down farther than if you were to just stand on it, once your velocity reaches zero however, you exhert no net force on the spring since your acceleration is 0 and anything times 0 equals... 0. so the spring can then force you back up
How do you calculate velocity of a box attached to a spring?
some basic physics will tell you that the mass of the box times acceleration due to gravity times the height of the box above the ground, minus the force of the spring or the spring constant times the distance the spring stretches will equal .5 times the mass of the box times the velocity squared mgh-kx=.5mv2
What is the extension of a stretched spring?
The amount the spring is stretched is called the displacement.
How do you work out the extension of a spring?
The amount the spring is stretched is called the displacement.
What is oscillation of a spring?
The oscillation of a spring is the motion that the spring makes when disturbed. Imagine holding the end of a spring and hanging a weight to the other end. If you do not disturb the weight, it will stay in a static position. However, when you pull down on the weight and let go, the spring "oscillates" up and down. The spring could also be compressed and released, creating the same effect. The up and down motion, which has a specific velocity and period relating to the spring constant k, is oscillation.
Is elastic force and spring force the same?
Elastic force is a function of stiffness and mass of a material, while gravitational force is the function of mass and acceleration of the material. Elastic force comes in to action when a body is moved from its equilibrium position. You know how spring works, when any displacement is given it tries to come back to its original shape and position. Its vibration decreases to zero when it comes to steady state. Where as in gravitational force, it exists due to magnetic force at the center of the earth ie- gravity. Any body that is steady is in equilibrium with gravitational pull of the earth. Its main function is acceleration which is a function of velocity and again that is the function of displacement per unit time. However when we consider theory of general relativity any object is referred with respect to the other and gravity is a part of theory of relativity.
What does the spring constant k mean?
The spring constant is a measure of stiffness - the ability to resist displacement under a load. It is denoted by K where F = kx where f = load force and x = displacement
