As we know that KE and PE is same at a given position
so we will have as a function of position given as

also the PE is given as function of position as

now it is given that
KE = PE
now we will have




so the position is 0.707 times of amplitude when KE and PE will be same
Part b)
KE of SHO at x = A/3
we can use the formula

now to find the fraction of kinetic energy



now since total energy is sum of KE and PE
so fraction of PE at the same position will be


The sun’s gravitational attraction and the planet’s inertia keeps planets moving is circular orbits.
Explanation:
The planets in the Solar System move around the Sun in a circular orbit. This motion can be explained as a combination of two effects:
1) The gravitational attraction of the Sun. The Sun exerts a force of gravitational attraction on every planet. This force is directed towards the Sun, and its magnitude is

where
G is the gravitational constant
M is the mass of the Sun
m is the mass of the planet
r is the distance between the Sun and the planet
This force acts as centripetal force, continuously "pulling" the planet towards the centre of its circular orbit.
2) The inertia of the planet. In fact, according to Newton's first law, an object in motion at constant velocity will continue moving at its velocity, unless acted upon an external unbalanced force. Therefore, the planet tends to continue its motion in a straight line (tangential to the circular orbit), however it turns in a circle due to the presence of the gravitational attraction of the Sun.
Learn more about gravity:
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Answer:
It is formed by a horizontal number line, called the x-axis, and a vertical number line, called the y-axis.
Explanation:
Answer:
KE₂ = 6000 J
Explanation:
Given that
Potential energy at top U₁= 7000 J
Potential energy at bottom U₂= 1000 J
The kinetic energy at top ,KE₁= 0 J
Lets take kinetic energy at bottom level = KE₂
Now from energy conservation
U₁+ KE₁= U₂+ KE₂
Now by putting the values
U₁+ KE₁= U₂+ KE₂
7000+ 0 = 1000+ KE₂
KE₂ = 7000 - 1000 J
KE₂ = 6000 J
Therefore the kinetic energy at bottom is 6000 J.
They almost entirely reside within galaxies because quasars are a subset of blackholes with a large and fast enough accretion disk to generate a beam of interstellar material perpendicular to itself. This typically only occurs in the largest black holes at the center of galaxies (supermassive blackholes) or at least stellar black holes---which still occur within galaxies because the material is necessary to form them.