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

${\log }_e\left[\frac{x_1}{x_{n+1}}\right]=a$

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