Question

A body in simple harmonic motion will have maximum velocity when its amplitude is

Answer 1

Hay mate here is your answer ✌❤☺



In simple harmonic motion displacement is directly proportional to acceleration.When the distance from the equilibrium point(where the body has to stop)decreases the acceleration also decreases about velocity we all know that velocity is inversely proportional to distance from equilibrium meaning as displacement increases the velocity decreases so when the body pass through the mean point the velocity is maximum and acceleration is 0.



 The most important thing to remember is that velocity is inversely proportional to displacement and acceleration is directly proportional to displacement.

Hope it will help you ☺❤

Answer 2

Given :

A body in simple harmonic motion .

To Find :

What will be its amplitude when its velocity is maximum.

Solution :

We know , general equation of displacement in SHM is given by :

$x=Asin(\omega t +\phi)$ ......1

Now , velocity is given by differentiation of displacement .

$v=\dfrac{dx}{dt}\\\\v=\dfrac{d(Asin(\omega t +\phi))}{dt}\\\\v=A\dfrac{sin(\omega t +\phi)}{dt}\\\\v=A\omega cos(\omega t+\phi)$

Now , velocity is maximum when $cos(\omega t+\phi)$ is maximum i.e $\omega t+\phi=0^o$ .

Now , displacement for angle $\omega t+\phi=0^o$

So , $sin\ 0^o=0$

Putting value of $sin\ 0^o=0$ in equation 1 , we get :

x = 0 units .

Therefore , amplitude of body is 0 units or the equilibrium position when its velocity is maximum .

Hence , this is the required solution .