Question

A mass of 70 kg is suspended from a spring of stiffness 80 N/mm. A dashpot is

fitted to the system and it is found that its amplitude diminishes to 10% of its

initial value after 5 complete oscillations. Find the damping force per unit

velocity and its critical value. Also find the frequency of vibration and compare

it with the frequency of free vibrations.​

Answer 1

Answer:

ANSWER

The natural frequency is given by

f

n

=

2π

1

M

k

⇒f

n

=

2π

1

5

4000

=4.5Hz

ω

n

=2πf

n

=9π=28.28rad/s

The damped frequency is given by

f=f

n

1−δ

2

=4.5×

1−0.04

=4.41Hz

ω=ω

n

1−δ

2

=28.28×

1−0.04

=27.71rad/s

The initial displacement is 50mm downwards so C=−50mm

and its displacement after 0.3sec is given by

x=Ce

−δω

n

t

cosωt=−50×e

−0.2×28.28×0.3

cos(27.71×0.3)

⇒x=−50×0.183×(−0.443)=4.07mm