An object is vibrating along the x-axis at a frequency of 4.04 Hz. The object ha
ID: 1488769 • Letter: A
Question
An object is vibrating along the x-axis at a frequency of 4.04 Hz. The object has a maximum speed of 0.445 m/s during Its vibration, and a phase constant of phi_0 = 0.223 rad. What is the equation of the x-component of the velocity of this object? What is the amplitude of the motion of this object? What is the maximum acceleration of the vibrating object? The equation above describes a 5-kg block attached to a spring, sliding along a frictionless surface What is the spring constant of the spring?Explanation / Answer
a)
f = frequency = 4.04 Hz
w = 2pi f = 2 x 3.14 x 4.04 = 25.4
Vmax = 0.445 m/s
phi = 0.223
equation for displacement is given as
X = A Cos(wt + phi)
taking derivative both side
V = - Aw Sin(wt + phi)
V = - Vmax Sin(wt + phi)
V = - 0.445 Sin(25.4 t + 0.223)
b)
Aw = 0.445
A (25.4) = 0.445
A = 0.0175
c)
maximum acceleration = Aw2 = 0.0175 (25.4)2 = 11.3
d)
w = sqrt (k/m)
25.4 = sqrt (k/5)
k = 3230