Advanced structural systems - mechanical engineering

Problem Set 1 – KB6005 – Free vibration of single-degree-of-freedom systems

1. Consider the mass-spring-damper system shown below. Show that the gravity does not affect

the natural frequency.

2. Obtain the natural frequency of the system shown below.

3. Obtain the equivalent spring constant of springs connected (a) in parallel and (b) in series.

(a): parallel

(b): series

Problem Set 1 – KB6005 – Free vibration of single-degree-of-freedom systems

4. Derive the equation of motion of the system shown below and obtain the natural frequency.

5. Obtain the damped natural frequency of the system shown below.

6. For the system shown below, derive the equation of motion and obtain the natural frequency.

Problem Set 1 – KB6005 – Free vibration of single-degree-of-freedom systems

7 (only for interested readers!). A helical spring of stiffness k is cut into two halves and a

mass m is connected to the two halves as shown below. Obtain the natural frequency of each

system in terms of k and m. Which system is stiffer?