Advanced structural systems - mechanical engineering
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ProblemSet1_Solution.pdf
Problem Set 1 Solution – 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.
Problem Set 1 Solution – KB6005 – Free vibration of single-degree-of-freedom systems
2. Obtain the natural frequency of the system shown below.
Problem Set 1 Solution – KB6005 – Free vibration of single-degree-of-freedom systems
3. Obtain the equivalent spring constant of springs connected (a) in parallel and (b) in series.
Problem Set 1 Solution – KB6005 – Free vibration of single-degree-of-freedom systems
Problem Set 1 Solution – 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.
Problem Set 1 Solution – KB6005 – Free vibration of single-degree-of-freedom systems
Problem Set 1 Solution – KB6005 – Free vibration of single-degree-of-freedom systems
Problem Set 1 Solution – KB6005 – Free vibration of single-degree-of-freedom systems
5. Obtain the damped natural frequency of the system shown below.
Problem Set 1 Solution – KB6005 – Free vibration of single-degree-of-freedom systems
Problem Set 1 Solution – KB6005 – Free vibration of single-degree-of-freedom systems
Problem Set 1 Solution – KB6005 – Free vibration of single-degree-of-freedom systems
Problem Set 1 Solution – KB6005 – Free vibration of single-degree-of-freedom systems
6. For the system shown below, derive the equation of motion and obtain the natural frequency.
Problem Set 1 Solution – KB6005 – Free vibration of single-degree-of-freedom systems
Problem Set 1 Solution – KB6005 – Free vibration of single-degree-of-freedom systems
Problem Set 1 Solution – 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?
Problem Set 1 Solution – KB6005 – Free vibration of single-degree-of-freedom systems
