ME 3253 – Linear System Theory
Prof. Nejat Olgac
Student Name
Homework # 1
Due date
September 5, 2012
The mass-spring setting, as shown on Figure 1, is to be studied.
g = 9.81 m/s2
m = 40 kg
k = 640 N/m
No friction
F(t)
x(t)
m
k
350
Figure 1: Mass – spring setting
F = 5sin(5t)
F = -5
F=0
t
3
2
3
t9
2
9  t  15
At the beginning (time t=0) the mass is at rest and spring is compressed. Find the motion x(t) and
plot it for 0  t  15 , when F(t) is varying in the following forms.
(a)
Without any math, how would you predict the motion of the mass m? Draw a rough plot
depicting the motion x(t) with respect to time. Give intuitive reasons for your plot.
(b)
Using the Newton’s second law and the free body diagram of the system, obtain the
governing equation of motion for mass m.
(c)
Solve part (b) using any Ordinary Differential Equation (ODE) solution method to obtain
an analytical expression for x(t).
(d)
Plot x(t) versus time t. Compare this result with part (a). Justify your comparison; but
please don’t redraw part (a) at this point.