CSAT APTITUDE
https://t.co/9DDyLxX7qA
Parabola has a general equation of the form aX^2+bX+c+0,having immense appln to find max/min pic.twitter.com/aqVFvWYQa1
— Abraham Malik (@brhmmlk93_malik) February 16, 2015
SHM: Stands for Simple Harmonic Motion .It's most important property is it's total mechanical Energy is conserved during its period of motion ie Sum(dK+dU)=constant .It's knowledge is mandatory to understand electromagnetic Radiation,Spring mass system and Antenna theory thus it is the key to understanding physical layer communication theory.
The projection of simple harmonic motion along x-axis and y-axis is A Cos(wt+phi) and along y-axis
A sin(wt+phi) .
Mathematically, the restoring force F is given byEquation for simple harmonic motion.
For one-dimensional simple harmonic motion, the equation of motion, which is a second-order linear ordinary differential equation with constant coefficients, could be obtained by means of Newton's second law (and Hooke's law for a mass on a spring).
Therefore,
Using the techniques of differential calculus, the velocity and acceleration as a function of time can be found:
Acceleration can also be expressed as a function of displacement:
and, since T = 1/f where T is the time period,
- The kinetic energy K of the system at time t is
- Simple harmonic motion can also be related to circular motion where the centripetal acceleration a=v^2/r =w^2.r is the restoring force acceleration responsible for circular periodic motion as for simple harmonic motion a restoring force towards the origin or center of circle is required.
Like all other motions of an object that can be modeled as a particle, circular motion is governed by Newton’s second law. The object’s acceleration toward the center of the circle must be caused by a force, or several forces, such that their vector sum
SUM(F) is a vector that is always directed toward the center, with constant
magnitude. The magnitude of the radial acceleration is given by
magnitude. The magnitude of the radial acceleration is given by
Circular motion of a mass attached by a thread is an example of simple harmonic motion and its free body diagram is given as following you can work out the conservative restoring force by free body diagram and tell me in the comment!
For reference you can see at .http://en.wikipedia.org/wiki/Simple_harmonic_motion.
https://www.youtube.com/watch?v=bmczI-3qSJw&feature=youtu.be
https://t.co/8cyR1up9JQ Gravitational field is the distortion of Space Time 4D fabric by mass m making plane convex d pic.twitter.com/MWkPlGK5U0
— Abraham Malik (@brhmmlk93_malik) February 8, 2015
http://advancedmathematicalresearch.blogspot.in/
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