Respuesta :
Answer:
x = 1.26 sin 3.16 t
Explanation:
Assume that the general equation of the displacement given as
x = A sinω t
A=Amplitude ,t=time ,ω=natural frequency
We know that speed V
[tex]V=\dfrac{dx}{dt}[/tex]
V= A ω cosωt
Maximum velocity
V(max)= Aω
Given that F= 32 N
F = K Δ
K=Spring constant
Δ = 0.4 m
32 =0.4 K
K = 80 N/m
We know that ω²m = K
8 ω² = 80
ω = 3.16 s⁻¹
Given that V(max)= Aω = 4 m/s
3.16 A = 4
A= 1.26 m
Therefore the general equation of displacement
x = 1.26 sin 3.16 t
Answer:
Explanation:
mass, m = 8 kg
extension, y = 0.4 m
force, F = 32 N
maximum velocity, v = 4 m/s
maximum velocity , v = ω A
where, ω be the angular velocity and A be the amplitude
4 = ω x 0.4
ω = 10 rad/s
position
x = A Sin ωt
x = 0.4 Sin 10 t
