Question

In the resonance curve, the natural frequency is where the _________ of the curve occurs,
A) Peak
B) Cusp
C) Foot
D) Any point

Answer 1

Hint: Natural frequency is the frequency attained when the amplitude of the wave reaches its maximum value. Eigen frequency is known as the natural frequency. And the resonance curve occurs when the amplitude of the curve reaches maximum. This increased amplitude happens when the frequency applied is equal to the natural frequency.

Complete step by step answer:
(i) The resonance curve is the curve whose amplitude reaches its maximum value. This increased amplitude is attained by the curve when the frequency applied is equal to the natural frequency.
(ii) So, we can say that the natural frequency at the abscissa attains when it meets maximum amplitude at the ordinate. We can say the point where the amplitude is maximum is “peak”.

Hence the correct answer is option A.

Additional information:
(i) The ‘cusp’ is the point in the curve at where the curve takes two opposite directions. Thus, the cusp is called a singular point in the curve. It is usually a ‘zero’.
(ii) A curve is a one-dimensional image that has only length not having a width, breadth, etc. The curves need not be straight. It has many shapes and many types. A cusp is one form of the curve and also the loop too.

Note:
The resonance curve is due to the curve attaining the natural frequency. The natural frequency can cause irreparable damage to the devices. The natural frequency causes the curve to attain the maximum amplitude. The amplitude is the maximum distance traveled by the curve. This is also the measure equal to one-half of the distance traveled by the curve.