Answer:
x(t) = - 6 cos 2t
Explanation:
Force of spring = - kx
k= spring constant
x= distance traveled by compressing
But force = mass × acceleration
==> Force = m × d²x/dt²
===> md²x/dt² = -kx
==> md²x/dt² + kx=0 ------------------------(1)
Now Again, by Hook's law
Force = -kx
==> 960=-k × 400
==> -k =960 /4 =240 N/m
ignoring -ve sign k= 240 N/m
Put given data in eq (1)
We get
60d²x/dt² + 240x=0
==> d²x/dt² + 4x=0
General solution for this differential eq is;
x(t) = A cos 2t + B sin 2t ------------------------(2)
Now initially
position of mass spring
at time = 0 sec
x (0) = 0 m
initial velocity v= = dx/dt= 6m/s
from (2) we have;
dx/dt= -2Asin 2t +2B cost 2t = v(t) --- (3)
put t =0 and dx/dt = v(0) = -6 we get;
-2A sin 2(0)+2Bcos(0) =-6
==> 2B = -6
B= -3
Putting B = 3 in eq (2) and ignoring first term (because it is not possible to find value of A with given initial conditions) - we get
x(t) = - 6 cos 2t
==>
Answer:
elliptical orbit
Explanation:
There are three laws of planetary motion, which are called Kepler's law of planetary motion.
First Law : It states that all the planets revolve around the sun in an elliptical path and the sun is at one focus of that elliptical path.
The angle at which the sunlight received at a location on Earth spread out over the largest area is 10°. Last option is correct.
<h3>What is sunlight?</h3>
The light coming from the Sun reaching the Earth's surface is called as Sunlight.
When the sun is overhead, the intensity is high because sun's rays are perpendicular to the earth's surface, so the energy spreads over a small area and the heat is too high in that region.
When, the angle is smaller, the sunlight will spread out over a larger area.
Thus, at 10° the sunlight received at a location on Earth spread out over the largest area. Last option is correct.
Learn more about Sunlight.
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Answer: 3- Large cells of rising and sinking gasses
Explanation: Hotter gas coming from the radiative zone expands and rises through the convective zone. It can do this because the convective zone is cooler than the radiative zone and therefore less dense. As the gas rises, it cools and begins to sink again. As it falls down to the top of the radiative zone, it heats up and starts to rise. This process repeats, creating convection currents and the visual effect of boiling on the Sun's surface.
