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

Logarithmic decrement is equal to 0.182

Step-by-step 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^{(1)/(n)}`

=
`ln\ 9^{(1)/(12)}`

=ln (1.2)

= 0.182

Hence, Logarithmic decrement is equal to 0.182