Answer:
the required solution is; x(t) = 0.675<em>sin</em>( 2.222t )
Explanation:
Given the data in the question;
Using both Newton's and Hooke's law;
m + k = 0, (0) = 0, (0) = 1.5
given that mass m = 9 kg
= 1.8 m
k is F / x
hence
k = F / x
given that, F = 80 N
we substitute
k = 80 / 1.8
k = 44.44
so
m + k = 0,
we input
9 + 44.44 = 0,
+ 4.9377 = 0
so auxiliary equation is,
r² + 4.9377 = 0
r² = -4.9377
r = √-4.9377
r = ±2.222i
hence, the solution will be;
x(t) = A×cos( 2.222t ) + B×sin( 2.222t )
⇒ (t) = -2.222Asin( 2.222t ) + 2.222Bcos( 2.222t )
using initial conditions
x(0) = 0
⇒ 0 = A
(t) = 1.5
1.5 = 2.222B
so
B = 1.5 / 2.222 = 0.675
Hence, the required solution is; x(t) = 0.675<em>sin</em>( 2.222t )
Answer:
They move at 2.8 m/s and in the opposite direction.
Explanation:
Answer:
A joule equals the amount of work done on an object when a force <u>of</u><u> </u><u>1</u><u> </u><u>Newton</u><u> </u> displaces that object <u>1</u><u> </u><u>metre</u>
Answer:
newton's third law of motion
Explanation:
The model of balloon car is example of newton's third law of motion which says that to every action there is always and equal and opposite reaction. As the balloon is inflated and then release the nozzle, the rubber contacts and pushes the air forward out of the nozzle, the air pushes back on the rubber and propelling the balloon forward.
Answer:
Direct variation suggests that two variables change in the same direction, when one variable decreases the other increases.