Answer

Verified

429.9k+ views

**Hint:-**A simple harmonic motion is a periodic motion in which there is a restoring force which is acting towards the equilibrium position of the body also the restoring force is proportional to the displacement of the body executing simple harmonic motion.

Formula used: The formula of acceleration of the body executing simple harmonic motion is given by,

${a_{\max .}} = A{\omega ^2}$

Where ${a_{\max .}}$ is the maximum acceleration of the body A is the amplitude of the body and $\omega $ is the angular frequency of the body.

**Complete step-by-step solution**

It is given in the problem that an object executing a simple harmonic motion has an amplitude of 0.01 m and the frequency of the simple harmonic motion is 40 Hz and we need to find the value of the maximum acceleration of the body executing simple harmonic motion.

As the angular frequency of the body is given by,

$\omega = 2\pi f$

Where $\omega $ is the angular acceleration and f is the frequency of the body is 40 Hz.

So the angular frequency is given by,

$ \Rightarrow \omega = 2\pi f$

$ \Rightarrow \omega = 2\pi \cdot \left( {40} \right)$

$ \Rightarrow \omega = 80\pi \dfrac{1}{s}$………eq. (1)

As the formula of maximum acceleration is given by,

${a_{\max .}} = A{\omega ^2}$

Where ${a_{\max .}}$is the maximum acceleration of the body, A is the amplitude of the body and $\omega $ is the angular frequency of the body.

Replacing the value of the amplitude A and the angular frequency of the body executing simple harmonic motion we can get the value of maximum acceleration of the body.

$ \Rightarrow {a_{\max .}} = A{\omega ^2}$

Replace the value of amplitude $A = 0 \cdot 01m$ and $\omega = 80\pi $ we get,

$ \Rightarrow {a_{\max .}} = \left( {0 \cdot 01} \right){\left( {80\pi } \right)^2}$

$ \Rightarrow {a_{\max .}} = 630\dfrac{m}{{{s^2}}}$.

The maximum acceleration is equal to${a_{\max .}} = 630\dfrac{m}{{{s^2}}}$. The correct answer for this problem is option A.

**Note:-**The maximum acceleration of the body executing simple harmonic motion is independent of the mass of the body also it is independent of the displacement of the body which is executing simple harmonic motion.

Recently Updated Pages

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

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

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

Trending doubts

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

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

Difference Between Plant Cell and Animal Cell

Which are the Top 10 Largest Countries of the World?

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

10 examples of evaporation in daily life with explanations

Give 10 examples for herbs , shrubs , climbers , creepers

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