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
==>
Explanation:
Given that,
Rate of cooling of air
Initial temperature= 80°C
Final temperature = 5°C
We need to calculate
Using newton's law of cooling
Where, 
Here, 
= 25°C (surrounding temperature)
dt = 1 minute
Put the value into the formula
Hence, This is the required answer.
<span>Which group in the periodic table is known as salt formers?
The correct option is the last one: Halogen family.
</span><span>
You can find the halogen or "</span>salt formers" in the group 17 of the periodic table. These are:
- Fluorine.
-Chlorine.
- Bromine.
- Iodine.
- Astatine.
All of them are non-metallic elements and they have 7 electrons.
Answer: Light passes through the front of the eye (cornea) to the lens. The cornea and the lens help to focus the light rays onto the back of the eye (retina). The cells in the retina absorb and convert the light to electrochemical impulses which are transferred along the optic nerve and then to the brain.
Explanation:
When light rays reflect off an object and enter the eyes through the cornea (the transparent outer covering of the eye), you can then see that object. The cornea bends, or refracts, the rays that pass through the round hole of the pupil.
If the car in the opposite direction turns the signal on your vehicle, then it is only likely to give way and let him or her turn before you make your turn because he or she is in the right of way and by doing this, it will prevent any complication from happening and to be able to show respect and politeness in driving.
