Respuesta :
Answer: a) v = - 0.698 m/s, b) k= 45 N/m, c) E = 0.009J
Explanation: From the question, we have the mass as 45g = 0.45kg
The position x(t) is given as
x(t) = 2.0 cos (10t).
Let us compare the equation with the general equation of a periodic motion, we have that
x(t) = A cos (ωt)
x(t) = 2.0 cos (10t)
A = amplitude = 2.0cm = 0.02 m
(ωt) = (10t)
Hence, ω = 10 rad/s
A)
To get the velocity, we find the first derivative of displacement x(t).
Hence dx(t) /dt = - 20 sin (10t) {chain rule was used in differentiating}
So therefore, v = - 20 sin (10t), at t =0.40s, we have v as
v = - 20 sin (10×0.40)
v = - 20 sin 4
v = - 0.698 m/s
The negative sign denotes that the velocity is in opposite direction to the displacement.
B)
The formulae that relates angular frequency, spring constant and mass of a loaded spring is given below as
ω = √k/m
Where k = spring constant, m = mass of object = 0.45kg, ω = 10 rad/s
By substituting the parameters
10 = √k/0.45
By squaring both sides
10² = k/ 0.45
100 = k/0.45
k = 100 × 0.45
k = 45 N/m
C)
The total energy of a loaded spring is given below as
E = 1/2 KA²
where A = amplitude = 0.02m
E = 1/2 ×45 × 0.02²
E = 0.018/2
E = 0.009 J
