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
==>
Friction can be bad by being too strong or too weak.
<span>Sometimes, when it is too strong, it decreases efficiency since some energy is wasted and turns to heat. Friction can also d</span><span>amage equipment/objects like when you slide it on the floor.
</span>
When friction is too weak, like for instance when there is black ice- our center of gravity is displaced too quickly and we can fall. Likewise, if there is a lot of slush on the ground, cars can slip and slide.
The modifications to the car design that would have the greatest effect on increasing the kinetic energy of the car is to increase the mass of the car slightly (option B).
<h3>What is kinetic energy?</h3>
Kinetic energy is the energy possessed by an object because of its motion. The kinetic energy equal (nonrelativistically) to one half the mass of the body times the square of its speed.
According to this question, an engineer is designing a small toy car that will be launched from rest. The engineer wants to maximize the kinetic energy of the car when it is launched by a compressed spring.
However, he can only make one adjustment to the initial conditions of the car. Considering the fact that the mass of an object is directly proportional to the kinetic energy.
This suggests that the modifications to the car design that would have the greatest effect on increasing the kinetic energy of the car is to increase the mass of the car slightly.
Learn more about kinetic energy at: brainly.com/question/12669551
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If it is a true or false question then it is true
D. write down the coefficients
