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 )
Top to bottom: C, B, D, A.
The answer is C. The Right yo a Speedy Trial. I just had that question and I got it right.
The resultant of the two vectors is determined as 9.1 units at 83.7⁰.
<h3>
Resultant of the vectors</h3>
The resultant of the vectors is calculated as follow;
Sum of vectors in x-direction = (3 - 2)x = x
Sum of vectors in y-direction = (5 + 4)y = 9y
Resultant vector = √(1² + 9²) = 9.1 units
Direction of the vectors = tan⁻¹(y/x) = tan⁻¹(9/1) = tan⁻¹(9) = 83.7⁰
Thus, the resultant of the two vectors is determined as 9.1 units at 83.7⁰.
Learn more about vectors here: brainly.com/question/25811261
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