A.lucid because it makes more sense yo the answer how about you do it yourself
Answer:
a) t=24s
b) number of oscillations= 11
Explanation:
In case of a damped simple harmonic oscillator the equation of motion is
m(d²x/dt²)+b(dx/dt)+kx=0
Therefore on solving the above differential equation we get,
x(t)=A₀
where A(t)=A₀
A₀ is the amplitude at t=0 and
is the angular frequency of damped SHM, which is given by,

Now coming to the problem,
Given: m=1.2 kg
k=9.8 N/m
b=210 g/s= 0.21 kg/s
A₀=13 cm
a) A(t)=A₀/8
⇒A₀
=A₀/8
⇒
applying logarithm on both sides
⇒
⇒
substituting the values

b) 

, where
is time period of damped SHM
⇒
let
be number of oscillations made
then, 
⇒
Answer:
Part a)

Part b)


Part c)


Explanation:
Part a)
frequency of light will not change with change in medium but it will depend on the source only
so here frequency of light will remain same in both water and glass and it will be same as that in air



Part b)
As we know that the refractive index of water is given as

so the wavelength in the water medium is given as



Similarly the refractive index of glass is given as

so the wavelength in the glass medium is given as



Part c)
Speed of the wave in water is given as



Speed of the wave in glass is given as



The data convincingly show that wave frequency does not affect wave speed. An increase in wave frequency caused a decrease in wavelength while the wave speed remained constant. The last three trials involved the same procedure with a different rope tension.