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 )
Answer:
13.5 m
Explanation:
First, convert km/h to m/s:
64 km/h × (1000 m / km) × (1 h / 3600 s) = 17.8 m/s
Distance = rate × time
d = 17.8 m/s × 0.761 s
d = 13.5 m
Answer:106.6N
Explanation:
Centripetal force is a force that cause a body to move along a circular path in a field. The body possesses a mass and velocity(since it's moving) and also radius alone the circular path on which it moves.
Given mass (m) = 2kg, velocity (v) = 8m/s and radius (r) = 1.2m
Centripetal acceleration(a)= v²/r
Centripetal force = ma = mv²/r
Substituting this values in the formula above we have;
Centripetal force = 2×8²/1.2m
Centripetal acceleration = 128/1.2
= 106.6N
