Answer:
a) x (t) = 0.3187 cos (7.416 t + 1.008)
, b) v = -2,363 sin (7,416 t + 1,008)
c) a = - 17.52 cos (7.416t + 1.008)
Explanation:
The spring mass system creates a harmonic oscillator that is described by the equation
x = Acos (wt + φ)
Where is the amplitude, w the angular velocity and fi the phase
a) Let's reduce the SI system
x = 17.0 cm (1 m / 100 cm) = 0.170 m
The angular velocity is given by
w = √ (k / m)
w = √ 11 / 0.200
w = 7.416 rad / s
Let's look for the terms of the equation with the data for time zero (t = 0 s)
0.170 = A cos φ
Body speed can be obtained by derivatives
v = dx / dt
v = -A w sin (wt + φ)
2.0 = -A 7.416 sin φ
Let's write the two equations
0.170 = A cos φ
2.0 / 7.416 = -A sin φ
Let's divide those equations
tan φ= 2.0 / (7.416 0.170)
φ= tan⁻¹ (1,586)
φ= 1.008 rad
We calculate A
A = 0.170 / cos φ
A = 0.170 / cos 1.008
A = 0.3187 m
With these values we write the equation of motion
x (t) = 0.3187 cos (7.416 t + 1.008)
b) the speed can be found by derivatives
v = dx / dt
v = - 0.3187 7.416 sin (7.416 t +1.008)
v = -2,363 sin (7,416 t + 1,008)
c) the acceleration we look for conserved
a = dv / dt
a = -2,363 7,416 cos (7,416 t + 1,008)
a = - 17.52 cos (7.416t + 1.008)
