Question

If a particle of mass m moves in a potential energy field u=u0-ax+bx^2 calculate time period

Answer 1

Answer:

Explanation:

Pls find your answer in the attachment below

Answer 2

Answer: The frequency is  

$f=\frac{1}{2\pi } (2b/m)^(0.5)$

Explanation:

Given that

If a particle moves in a potential energy field U = Uo-ax+bx² , where a and b are positive constant

We know that       Force= -(dU/dx)

Where

U : Potential Energy

So, according to question,

F=-(d(Uo-ax+bx^2 )/dx)

F= a-2bx ………(1)

From equation 1, we found that force is Zero at x = a/2b

Now, we will find out (d^2 U)/(dx^2 )     at x=a/2b

At (d^2 U)/(dx^2 )  =2b>0   at x=a/2b

That means, potential energy is minimum at x= a/2b

And k=2b

So, frequency is

$f=\frac{1}{2\pi } (k/m)^(0.5)$

$f=\frac{1}{2\pi } (2b/m)^(0.5)$

Where pi= 3.14