Answer

Verified

345.9k+ views

**Hint:**SHM stands for Simple Harmonic Motion, which is characterised as a motion in which the restoring force is proportional to the body's displacement from its mean location. This restoring force often moves in the direction of the mean location. The acceleration of a particle in simple harmonic motion is given by \[a\left( t \right){\text{ }} = {\text{ }} - {\omega ^{2\;}}x\left( t \right)\] . Here, is the particle's angular velocity.

**Complete step-by-step solution:**

Simple harmonic motion is an oscillatory motion in which the particle's acceleration is directly proportional to its displacement from the mean position at any stage. It's a form of oscillatory motion that's a little different.

Simple Harmonic Motions (SHM) are oscillatory and periodic in nature, but not all oscillatory motions are SHM. The harmonic motion of all oscillatory motions, the most common of which is simple harmonic motion, is known as oscillatory motion (SHM).

The displacement, velocity, acceleration, and force in this form of oscillatory motion differ (with respect to time) in a way that can be represented by either sine (or) cosine functions, collectively known as sinusoids.

Now, coming to the question;

$K.E = P.E$

$ \Rightarrow \dfrac{1}{2}m{\omega ^2}({A^2} - {x^2}) = \dfrac{1}{2}m{\omega ^2}{x^2}$

$ \Rightarrow {A^2} - {x^2} = {x^2}$

$ \Rightarrow 2{x^2} = {A^2}$

$\therefore x = \dfrac{A}{{\sqrt 2 }}$

$2A = 8$

$A = \dfrac{8}{2} = 4cm$

$x = \dfrac{A}{{\sqrt 2 }}$

$x = \dfrac{4}{{\sqrt 2 }} = \sqrt[2]{2}$

**So, the correct option is: (C) $\sqrt[2]{2}cm$.**

**Note:**Simple Harmonic Motion is a very useful and important method for understanding the properties of sound waves, light waves, and alternating currents. Any non-simple harmonic oscillatory motion can be expressed as a superposition of several harmonic oscillatory motions of different frequencies.Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

The 3 + 3 times 3 3 + 3 What is the right answer and class 8 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

How many crores make 10 million class 7 maths CBSE

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Change the following sentences into negative and interrogative class 10 english CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE