Question

A box of 100 gm is attached to one end of a spring whose other end is fixed to a rigid support. When a mass of 900 gm is placed inside the box, the system performs 4 vibrations per second and the amplitude falls from 2 cm to 1cm in 15 secs. Calculate the 1) force constant 2) relaxation time 3) Q factor of the system. ​

Answer 1

Explanation:

The body is released from rest when the spring is unstretched.

Hence, initial total energy is zero. Also, total energy remains conserved.

E

i

=E

f

E

i

=U

spring

+U

gravity

+KE

f

0=

2

1

×10×(0.15)

2

−0.1×10×0.15+

2

1

×0.1×v

2

∴v=0.866 m/s