Answer:
Explanation:
F = Force = 
m = Mass of proton = 
t = Time taken = 
Acceleration is given by
The velocity of the proton is
Answer:
equation of motion for the mass is x(t) = e^αt ( C1 cos √{α² - ω²} t + C2 sin √{α² - ω²} t )
Explanation:
Given data
mass = 3 slugs = 3 * 32.14 = 96.52 lbs
constant k = 9 lbs/ft
Beta = 6lbs * s/ft
mass is pulled = 1 ft below
to find out
equation of motion for the mass
solution
we know that The mass is pulled 1 ft below so
we will apply here differential equation of free motion i.e
dx²/dt² + 2 α dx/dt + ω² x =0 ........................1
here 2 α = Beta / mass
so 2 α = 6 / 96.52
α = 0.031
α² = 0.000961 ...............2
and
ω² = k/mass
ω² = 9 /96.52
ω² = 0.093 ..................3
we can say that from equation 2 and 3 that α² - ω² = -0.092239
this is less than zero
so differential equation is
x(t) = e^αt ( C1 cos √{α² - ω²} t + C2 sin √{α² - ω²} t )
equation of motion for the mass is x(t) = e^αt ( C1 cos √{α² - ω²} t + C2 sin √{α² - ω²} t )
The acceleration of the given wave is 2.5m/s^2
<h3>Wave property</h3>
The standard wave function is expressed according to the equation
y = Asin(2πft+2πx/λ)
where
λ is the wave length
Given the equation below
y = 0.120 sin((π/8)x + 4πt)
Compare both equation to have:
(π/8)x = 2πx/λ
8 = 2/λ
λ = 2/8
λ = 1/4
λ = 0.25m
For the frequency
Compare both equation to have:
4πt = 2πft
4 = 2f
4/2 = 2f/2
f = 2 Hz
Speed = fλ
speed = 2(0.25)
speed = 0.5m/s
Determine the acceleration
acceleration = change in velocity/time
acceleration = 0.5/ 0.200
acceleration = 2.5m/s^2
Hence the acceleration of the given wave is2.5m/s^2
Learn more on wave function here: brainly.com/question/25699025
#SPJ4
Answer:
Immune system
Explanation:
Because they defense our body act as 'Police of the body'.
