A) 
The total energy of the system is equal to the maximum elastic potential energy, that is achieved when the displacement is equal to the amplitude (x=A):
(1)
where k is the spring constant.
The total energy, which is conserved, at any other point of the motion is the sum of elastic potential energy and kinetic energy:
(2)
where x is the displacement, m the mass, and v the speed.
We want to know the displacement x at which the elastic potential energy is 1/3 of the kinetic energy:
Using (2) we can rewrite this as
And using (1), we find
Substituting 
into the last equation, we find the value of x:
B) 
In this case, the kinetic energy is 1/10 of the total energy:
Since we have
we can write
And so we find:
Answer: Wernicke's aphasia
Explanation:
John recently suffered a blow to his head. Since then, he finds it difficult to comprehend what others say to him. He also finds it difficult to express his thoughts and cannot seem to find the right words to say while speaking. However, he can speak freely with proper syntax. In this scenario, John is most likely suffering from Wernicke's aphasia.
Wernicke's aphasia occurs when the leftward side of the middle of the brain is damaged or has been altered. An individual who suffers from Wernicke's aphasia will have difficulty in speaking in meaningful and coherent sentences or may have difficulty in understanding the speech of others.
Measuring density: Measure the mass (in grams) of each mineral sample available to you. The mass of each sample is measured using a balance or electronic scale. Record mass on a chart.
Answer:
Inductance, L = 0.0212 Henries
Explanation:
It is given that,
Number of turns, N = 17
Current through the coil, I = 4 A
The total flux enclosed by the one turn of the coil, 
The relation between the self inductance and the magnetic flux is given by :
L = 0.0212 Henries
So, the inductance of the coil is 0.0212 Henries. Hence, this is the required solution.
It is given that for the convex lens,
Case 1.
u=−40cm
f=+15cm
Using lens formula
v
1
−
u
1
=
f
1
v
1
−
40
1
=
15
1
v
1
=
15
1
−
40
1
v=+24.3cm
The image in formed in this case at a distance of 24.3cm in left of lens.
Case 2.
A point source is placed in between the lens and the mirror at a distance of 40 cm from the lens i.e. the source is placed at the focus of mirror, then the rays after reflection becomes parallel for the lens such that
u=∞
f=15cm
Now, using mirror’s formula
v
1
+
u
1
=
f
1
v
1
+
∞
1
=
15
1
v=+15cm
The image is formed at a distance of 15cm in left of mirror
