(Solved): Part A-Beam system 1. Run the beam experiment in the Lab for the primary beam only. 2. Calculate th ...

Part A-Beam system 1. Run the beam experiment in the Lab for the primary beam only. 2. Calculate the natural frequency ${?}_n$ of the beam by using ${?}_n=\sqrt{\frac{k_b}{m1}}\text{, where }m1\text{ is the mass }171\mathrm{g}$ $k_b$ is the stiffness of the primary beam $=\frac{192EI}{L^3}$, where $\mathrm{E}$ is modulus of elacticity (70 GPa for aluminum ) $I=\frac{b{h}^3}{12}$, where beam width $\mathrm{b}=63\mathrm{mm}$, beam thickness $\mathrm{h}=4.5\mathrm{mm}$ and beam length $\mathrm{L}=920\mathrm{mm}$. 3. Add the auxiliary system (small beam mass) of a mass $m2=33\mathrm{g}$, and calculate how much the beam length should be to be perfectly tuned. Take $b=20\mathrm{mm},\mathrm{h}=1\mathrm{mm},\mathrm{E}=200$ GPa. 4. Discuss the obtained Lab results, when the auxiliary beam (the small beam) is added. Part B-Linear system 1. Run the linear spring experiment of $1\mathrm{DOF}$ (primary mass). 2. Calculate the natural frequency ${?}_n$ using $\mathrm{k}=300\mathrm{N}/\mathrm{m},\mathrm{m}=171\mathrm{g}$ 3. Add the auxiliary mass-spring system of the same $\mathrm{m}$ and $\mathrm{k}$ (same natural frequency). 4. Discuss the obtained Lab results, when the auxiliary system is added. Discuss if the system in this case is perfectly tuned.