Question

A single-degree-of-freedom mass-spring-damper system is observed during its free vibration and the displacement amplitude decays by 9 dB from its initial value after 12 cycles. The mass of the system is 7 kg and the spring stiffness is 3,000 N/m. Calculate the logarithmic decrement

Answer 1

Answer:

Logarithmic decrement is equal to 0.182

Explanation:

given,

amplitude decay = 9 dB          

number of cycles = 12 cycles        

mass of the system = 7 kg        

spring stiffness = 3000 N/m            

logarithmic decrement = ?                  

now,                                                      

logarithmic decreament = $ln\ D^{\frac{1}{n}}$

                                        = $ln\ 9^{\frac{1}{12}}$

                                        =ln (1.2)

                                        = 0.182

Hence, Logarithmic decrement is equal to 0.182