The Doppler effect is the right concept to solve this problem. The Doppler effect is understood as the change in apparent frequency of a wave produced by the relative movement of the source with respect to its observer. Mathematically it can be described as,

Here,
= Frequency of the sound from the Whistle
f = Frequency of sound heard
v = Speed of the sound in the Air
Replacing we have that





Therefore the minimum speed to know if the whistle is working is 16.33m/s
Answer:
a)
b)
c) 
d)
e)
Explanation:
1) Important concepts
Simple harmonic motion is defined as "the motion of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's Law (F=-Kx). The motion experimented by the particle is sinusoidal in time and demonstrates a single resonant frequency".
2) Part a
The equation that describes the simple armonic motion is given by
(1)
And taking the first and second derivate of the equation (1) we obtain the velocity and acceleration function respectively.
For the velocity:
(2)
For the acceleration
(3)
As we can see in equation (3) the acceleration would be maximum when the cosine term would be -1 and on this case:

Since we know the amplitude A=0.002m we can solve for
like this:

And we with this value we can find the period with the following formula

3) Part b
From equation (2) we see that the maximum velocity occurs when the sine function is euqal to -1 and on this case we have that:

4) Part c
In order to find the total mechanical energy of the oscillator we can use this formula:

5) Part d
When we want to find the force from the 2nd Law of Newton we know that F=ma.
At the maximum displacement we know that X=A, and in order to that happens
, and we also know that the maximum acceleration is given by::

So then we have that:

And since we have everything we can find the force

6) Part e
When the mass it's at the half of it's maximum displacement the term
and on this case the acceleration would be given by;

And the force would be given by:

And replacing we have:

This graph shows data up to about 2010. So it couldn't have been drawn before 2010. OF COURSE the data from only 10 years earlier was more reliable than the data that was 120 years old ! It wasn't even measured the same way back then as it is now.
Answer: The two answers are in explanation.
Explanation: Please find the attached files for the solution
Answer:
Explanation:
mass, m = 1400 kg
height, h = 16 m
initial velocity, u = 21 m/s
final velocity, v = 13 m/s
Work done by engine, We = 80 kJ
Let the work done by the friction force is Wf.
Use the work energy theorem
net work done = change in kinetic energy
work done by engine + work done by friction force + work done by the gravitational force = Change in kinetic energy
80000 + Wf - m x g x h = 0.5 m ( v² - u²)
80000 + Wf - 1400 x 9.8 x 16 = 0.5 x 1400 x ( 169 - 441 )
- 139520 + Wf = - 190400
Wf = 50880 J