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:
B. A collision scene
Explanation:
It could have been a parade ceremony, but, if you notice the vehicle's hazard lights or an emergency vehicle ahead, it is common sense to figure that they is a collision scene nearby.
Answer:
The same amount of energy is required to either stretch or compress the spring.
Explanation:
The amount of energy required to stretch or compress a spring is equal to the elastic potential energy stored by the spring:
where
k is the spring constant
is the stretch/compression of the spring
In the first case, the spring is stretched from x=0 to x=d, so
and the amount of energy required is
In the second case, the spring is compressed from x=0 to x=-d, so
and the amount of energy required is
so we see that the amount of energy required is the same.
Answer:
<u>Explanation:</u>
A linear equation is of the form: y = mx + b where
- m is the slope
- b is the y-intercept (where it crosses the y-axis)
x + 4y = 16
4y = -x + 16
The y-intercept (b) = 4
Next, find the slope given point (4, 5) and b = 4
Answer:
B
Explanation:
Because vector Y is longer than vector X
so when you take a magnitude( without minus ) each other
you see that Y>X