![]() Now, let us consider that if b=0, that means there is no damping and becomes a Simple Harmonic Motion. The time period of the damped simple harmonic oscillator is given by the expression So, mathematically, the angular frequency of the damped simple harmonic oscillator is given by the expression In the above expression, the damping is caused by the term e -bt/2m Therefore, by Newton’s laws of motion applied along the direction of the motion, we haveĪfter solving the above differential equation, we get the equation of the Damped Simple Harmonic Oscillator. Now, let the acceleration of the oscillating body at any time t be a(t). Total force Ftotal = F s + F d = -kx – bv The total net force then will be the summation of both the restoring and damping force. One is the Restoring force and the other is the Damping force. The motion of the oscillating body then slows down due to some external forces. When it is set in motion, it will start to and fro motion about its equilibrium position. Let us again consider the example of an oscillating body such as a pendulum. Equation for a Damped Simple Harmonic Oscillator As a result, the corresponding energy dissipation would also be much faster. ![]() If the oscillating body is immersed in a liquid, the magnitude of the damping force would be much higher. The damping force is dependent on the nature of its surrounding medium. V is the velocity of the oscillating body, and -b is the damping constant which depends on the characteristics of the medium i.e, shape, size, viscosity etc. Thus, we can form the expression as given below: So, the magnitude of the damping force is directly proportional to the velocity of the oscillating body. It always acts in a direction opposite to the direction of motion or velocity. But the oscillations remain approximately periodic for a small damping. The damping force is the one which opposes the motion of the oscillating body.
0 Comments
Leave a Reply. |