Question

A spring-mass-damper instrument is employed for acceleration measurements. The spring constant is 12000 N/m. The mass is 5 g. The damping ratio is 0.4.

Required:
a. Find natural frequency (in Hz) of this instrument.
b. Determine the bandwidth of this instrument in Hz
c. How can you increase the bandwidth of this instrument?

Answer 1

a) 246.56 Hz

b) 203.313 Hz

c) Add more springs

Step-by-step explanation:

Spring constant = 12000 N/m

mass = 5g = 5 * 10^-3 kg

damping ratio = 0.4

a) Calculate Natural frequency

Wn = √k/m =
`\sqrt{12000 / 5*10^(-3) }`

= 1549.19 rad/s ≈ 246.56 Hz

b) Bandwidth of instrument

W / Wn =
`√(1-2(0.4)^2)`

W / Wn = 0.8246

therefore Bandwidth ( W ) = Wn * 0.8246 = 246.56 * 0.8246 = 203.313 Hz

C ) To increase the bandwidth we have to add more springs