The train’s average speed is 80km/h
Answer:
The relationship between the initial stored energy
and the stored energy after the dielectric is inserted
is:
c) 
Explanation:
A parallel plate capacitor with
that is connected to a voltage source
holds a charge of
. Then we disconnect the voltage source and keep the charge
constant . If we insert a dielectric of
between the plates while we keep the charge constant, we found that the potential decreases as:

The capacitance is modified as:

The stored energy without the dielectric is
The stored energy after the dielectric is inserted is:

If we replace in the above equation the values of V and C we get that


Finally

By definition, we have that the work done is given by:

Where,
F: force in the direction of displacement
d: displaced distance
Substituting values we have:

Then, the power is given by:

Where,
t: time
Substituting values we have:


Answer:
The work done on the box is 100 Nm, and the power is 20 Nm/s.
Answer:
Part a)

Part b)

Explanation:
Part a)
as the mass of the suspension system is given as

also we have

so now for force balance we have



Part b)
Now we know that amplitude decreases by 63% in each cycle
so after one cycle the amplitude will become 37% of initial amplitude
so it is given as

also we know




here t = time period of one oscillation
so it is



now damping constant is


I'm not sure about the "in nature" part but i think its A