Practice Problems
1. Find the equivalent spring constant of the system shown in the in the direction of the
load P.
2. Consider a spring of stiffness k stretched by a distance x0 from its free length. One end
of the spring is fixed at point O and the other end is connected to a roller as shown in the
Figure. The roller is constrained to move in the horizontal direction with no friction. Find
the force (F)-displacement (x) relationship of the spring when the roller is moved by a
horizontal distance x to position B. Discuss the resulting force-displacement relation and
identify the stiffness constant k along the direction of x.
3.
4.0
5.0
6.0
7.0
8.0
9.0
10. Find out when case number when the natural frequency will be the maximum and their
corresponding EOM. Assume all the values of Mass, and Stiffness if necessary.
11.
12.0
13.0
14.0
15.0
16.0
17.
18.
19.
20.0
21.0 Write the differential equation of motion for the system shown in the Figure.
Determine the natural frequency of the damped oscillation and the critical damping
coefficient. Given: a= 1.75 m, b= 2.0m. m= 2 kg, k= 2 N/m