Class 11 NEET Physics Oscillations Questions

This is a case of damped vibration as the amplitude of vibration is decreasing with time.
Amplitude of vibrations at any instant t is given by a=a0e−bt, where a0 is the initial amplitude of vibrations and b is the damping constant.
Now, when t=100T,a=

a0

3

[T is time period ]
Let the amplitude be a′ at t=200T
.i.e. after completing 200 oscillations.
∴a=

a0

3

=a0e−100Tb .....(i)
and a′=a0e−200Tb .....(ii)
From (i),

1

3

=e−100Tb ∴e−200Tb=

1

9

From(ii), a′=a0×

1

9

=

a0

9

therefore The amplitude will be reduced to

1

9

of initial value.