s/n Particular Equation Calculated values (Belt and Pulley system) Calculated values (coupling system) With isolator Without isolator With isolator Without isolator 1 Ratio of consecutive amplitude $\frac{{x}_{1}}{{x}_{n+1}}$ 1.588235294 1.20 1.114836547 1.048171276 Logarithmic decrement ${\mathrm{log}}_{e}\left[\frac{{x}_{1}}{{x}_{n+1}}\right]=a$ 4.895102885 3.320116923 3.049069757 2.852430037 Operating frequency (rad/s) $\omega =\frac{2\pi N}{60}$ 50π 50π 50π 50π Natural frequency (rad/s) ${\omega }_{n}=\frac{\omega }{{f}_{r}}$ 25π 12,5π 12,5π 12,5π Damping frequency (rad/s) ${\omega }_{d}=\sqrt{{\omega }_{n}^{2}-{a}^{2}}$ 78.38711712 39.12930502 39.15135836 39.16617585 Isolator resistance to vibration (Ns/m) $c=2\cdot a\cdot {m}_{m}$ 244.7551443 166.0058462 152.4534879 142.6215019 Damped-undamped frequency ratio $\frac{{\omega }_{d}}{{\omega }_{n}}={f}_{d/u}$ 0.4990278866 0.9964195702 0.9969811538 0.9973584782 Periodic time (second) ${t}_{p}=\frac{2\pi }{{\omega }_{d}}$ 0.1612577416 0.1605749273 0.1604844779 0.1604237629 Static deflection (mm) $\frac{mg}{{k}_{is}}={\delta }_{st}$ 1.728208019 1.728208019 Transmitted force Reduction (%) $\left\{\frac{{\left(\frac{2\pi {N}_{o}}{60}\right)}^{2}\frac{m}{{k}_{is}}-2}{{\left(\frac{2\pi {N}_{o}}{60}\right)}^{2}\frac{m}{{k}_{is}}-1}\right\}=R$ 99.90838315 99.82796470 99.94821063