Newton's First Law states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force.
When two mechanical waves that have positive displacements from the equilibrium position meet and coincide, a constructive interference occurs.
Option A
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Explanation:</u></h3>
Considering the principle of superposition of waves; the resultant amplitude of an output wave due to interference of two or more waves at any point is given by individual addition of their amplitudes at that point. Two waves with positive displacements refer to the fact that crest of the both the waves are on the same side of displacement axis, either both are positive or both are negative, similarly with their troughs.
If such two waves with their crest on crest meet at any point, by superposition principle. their individual amplitude gets added up and hence the resultant wave after interference is greater in amplitude that both the individual waves. This is termed as a constructive interference. Destructive interference on the other hand is a condition when one of the two waves has a positive displacement and other has a negative displacement (a condition of one’s crest on other’s trough); resulting in amplitude subtraction.
Explanation:
Show that the motion of a mass attached to the end of a spring is SHM
Consider a mass "m" attached to the end of an elastic spring. The other end of the spring is fixed
at the a firm support as shown in figure "a". The whole system is placed on a smooth horizontal surface.
If we displace the mass 'm' from its mean position 'O' to point "a" by applying an external force, it is displaced by '+x' to its right, there will be elastic restring force on the mass equal to F in the left side which is applied by the spring.
According to "Hook's Law
F = - Kx ---- (1)
Negative sign indicates that the elastic restoring force is opposite to the displacement.
Where K= Spring Constant
If we release mass 'm' at point 'a', it moves forward to ' O'. At point ' O' it will not stop but moves forward towards point "b" due to inertia and covers the same displacement -x. At point 'b' once again elastic restoring force 'F' acts upon it but now in the right side. In this way it continues its motion
from a to b and then b to a.
According to Newton's 2nd law of motion, force 'F' produces acceleration 'a' in the body which is given by
F = ma ---- (2)
Comparing equation (1) & (2)
ma = -kx
Here k/m is constant term, therefore ,
a = - (Constant)x
or
a a -x
This relation indicates that the acceleration of body attached to the end elastic spring is directly proportional to its displacement. Therefore its motion is Simple Harmonic Motion.
