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What is a mass' maximum displacement from it's equilibrium position?
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What is the amplitude when you are given the mass and period and position of the oscillator and the velocity of the oscillator?
amplitude is the maximum displacement right from the equilibrium position. It does not depend on the mass, period or velocity. Recall displacement at any instant t is y = A sin 2 pi f t or A sin 2 pi t/T f = frequency and T - time period.
When are the displacement velocity and acceleration equal to zero for the motion of a mass on a spring?
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.
Can Elastic potential energy be converted to gravitational potential energy?
Yes. For example when a mass hung to a spring is displaced downwards from its equilibrium position, it oscillates and at the maximum height, the body has gained gravitational Ep compared to its initial position.
If the initial displacement from equilibrium amplitude is changed does the period of oscillation change?
Initial displacement has no effect on the period of oscillation. The period T = 2(pi)sqrt(mass/spring constant)
What quantities are involved in motion?
position, displacement, time, velocity, acceleration, force, mass
What is the amplitude when you are given the mass and period and position of the oscillator and the velocity of the oscillator?
amplitude is the maximum displacement right from the equilibrium position. It does not depend on the mass, period or velocity. Recall displacement at any instant t is y = A sin 2 pi f t or A sin 2 pi t/T f = frequency and T - time period.
How does a pendulums period vary with the length of its mass With Gravitational acceleration?
The length of the pendulum is measured from the pendulum's point of suspension to the center of mass of its bob. Its amplitude is the string's angular displacement from its vertical or its equilibrium position.
When are the displacement velocity and acceleration equal to zero for the motion of a mass on a spring?
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.
How do the different forms of potential energy depend on an objects position?
Potential energy of a body with certain mass is proportional to the vertical position of the body with respect to the ground. Potential energy of the string is proportional to second degree of displacement from the point of equilibrium.
What is effective action?
The mass action effect is the shift in the position of equilibrium through the addition or removal of a participant in the equilibrium.
What does equilibrium and equilibrium mixture mean?
A quantity that characterizes the position of equilibrium for a reversible reaction; its magnitude is equal to the mass action expression at equilibrium. K varies with temperature.
Can Elastic potential energy be converted to gravitational potential energy?
Yes. For example when a mass hung to a spring is displaced downwards from its equilibrium position, it oscillates and at the maximum height, the body has gained gravitational Ep compared to its initial position.
If the initial displacement from equilibrium amplitude is changed does the period of oscillation change?
Initial displacement has no effect on the period of oscillation. The period T = 2(pi)sqrt(mass/spring constant)
What quantities are involved in motion?
position, displacement, time, velocity, acceleration, force, mass
What affects a pendulum?
The mass of the pendulum, the length of string, and the initial displacement from the rest position.
Is the period of a vibrating spring linearly affected by the mass of the attached object?
Let a mass m be attached to the end of a spring with spring constant k. The spring extends and comes to rest with an equilibrium extension e. At equilibrium; Weight = Force exerted by spring => mg = ke -------- 1 Suppose the spring is displaced through a displacement x downwards from its equilibrium position: Resolving vertically, we have; Resultant force on mass = Force exerted by spring - Weight of mass => ma = k(e + x) - mg ------- 2 From 1, we have: ma = mg + kx - mg => a = (k/m)x Since a is proportional to displacement from equilibrium position, the oscillation is simple harmonic. So, (angular velocity)2 = (k/m) => 2pi/T = (k/m)1/2 => T = 2pi (m/k)1/2 This equation shows that the time period is proportional to the square root of the mass of the attached object.
Is the acceleration of a simple harmonic oscillator ever zero if so where?
Yes; the acceleration is zero when the velocity is at its maximum, that is, at the equilibrium position. Since the force and hence the acceleration always act TOWARDS the equilibrium position (because it's a restorative force), then the force and acceleration must change their sign as the mass crosses the e.p., and therefore must be zero instantaneously at the e.p.
