Vibration
Problem 1
KI
K2
M
m
f(t)
C
x(t)
x2(1)
a. Find the FBD for the system above. Label all relevant forces and set your coordinate system.
b. From the FBD, derive your equation of motion.
c. Given that the forcing function f is a sinusoidal function with a wave speed of 16 m/s, a wavelength of 4 meters, an amplitude of 500 meters, and a phase shift of π/2 radians, find the total solution for x(t) using the ODE that finds explicitly, if x(t) is given as sin(8t). Note that the trigonometric identity to be used to simplify your result is sin(a + b) = sin(a)cos(b) + cos(a)sin(b). It is safe to assume that x₀ = 0 m and x₀' = 0 m. Let m = 100 kg, K = 7200 N/m, and C = 1700 Ns/m.