**Article By: Dr. Anees Rasheed Khan, Amravati****Jr. College Lecturer (Physics)**

Now acceleration is given by,

Now velocity is given by,

Now, let the spring constant is ‘K’ then the force of stretching produced in the spring is given by,

Putting this value in equation (2) we get,

This is the differential equation for the oscillatory motion of a block attached with a spring. By solving this differential equation we can get the solution for the value of displacement ‘x’ as follows,

Here A is amplitude (maximum value of displacement) of oscillations of the block on the frictionless surface.

The voltage (induced emf) across the inductor is given by,

The overall potential in the tank circuit is conserved. It means that the sum of all potentials in the circuit will be zero.

Now, using the concept of electric current, we have

Putting this value in equation (1), we get

This is the differential equation for the electrical oscillations of LC tank circuit. By solving this differential equation we can get the solution for the value of charge ‘q’ as follows,

From the above two totally different areas of Physics, we have studied the use of Differential Equations in Physics. Hence the study of Differential Equations and their solutions are of great importance in Physics.

## Please sign-in to post comments

## Shiven Dhania

The three equation of motion by Sir Isaac Newton Are:

[1] v=u+at

[2] s=ut+1/2at(t)

[3] 2as=v(v)-u(u)

Where;

v final velocity

u initial velocity

a acceleration

t time

s displacement

Posted on : 03-05-2018 12:21:03