What are the conditions of Simple harmonic motion?

Answer 1

Simple harmonic motion is what we might say is happening when an object is in some non-complex periodic way. That is, the object experiences a force that displaces it, the displacement occurs and reaches some maximum value, and then the object returns to the "original" conditions and repeats the process. Let's take the example of a pendulum and consider what is happening.

The pendulum is started, and it swings (accelerates) down under the influence of gravity. At the bottom of its arc, it then swings up on the other side. It continues to move up (and decelerate) until it stops. The pendulum then begins to swing back down, reach some maximum velocity and the bottom of its arc, and then it swings back up to where it began. The pendulum has gone through one complete cycle of its motion, and because it is a repetitive cycle, it can be said to be simple harmonic motion. Frictional loss due to air and suspension components will eventually stop the pendulum, but we can use a small spring to off set this and keep the pendulum in fairly constant motion. You probably recognize this as the mechanism that is used in a clock.

The example of a spring may also be helpful. A spring with a weight is hanging from a support. The spring is pulled down slightly and released. The spring wants to return to its original position, and it pulls the weight up. That spring wants to return to its original position. But the weight "gathers" energy, and the spring is slightly compressed as the weight comtinues up past where the spring would like to have stopped. The weight finally does stop, and it starts back down. And (as you guessed), that weight goes past the point where the spring would like to have stopped, and it stretches it out again. The cycle will repeat, and only a bit of friction in air and in the spring will stop it eventually. As it continues to move, however, the weight and spring exhibit simple harmonic motion. The movement follows a fixed course and occurs over a given time, thus making this another example of repititious or periodic motion.

Whether it's a guitar string, a bouncing ball or something else that behaves in a similar way, they all can serve as examples of simple harmonic motion. A link can be found below for further understanding of simple harmonic motion, and the mathematics (which were omitted from this explanation) are included there. We'll also find the idea of the period of that motion (the amount of time required for a complete cycle of that motion) is introduced. The idea of amplitude, which speaks to the amount of displacement of the object or thing in periodic motion will also be presented. All of this is one mouse click away, and the curious investigator will make the jump.

Answer 2

a body is said to be in shm if it moves to and fro motion along a stringht line above its mean position such that at any point its acceleration is directly proportional to its displacement but opposite in direction and acceleration is always directed towards mean position

 

  if a is acceleration  of the body at any given displacement by form mean position then for the body to be in s.h.m

Answer 3

Simple Harmonic Motion is any motion where the force on the object in motion is always toward one point (the center of the motion) and depends on how far the object is from that point.

A playground swing or clock pendulum are fine examples.

Answer 4

That energy be added to the system in such a way as it is in synchrony with the oscillation. And usually, only enough energy is added to make up for that lost in friction etc.

Answer 5

Simple harmonic motion follows the same pattern as the projection of uniform circular motion, for example, on the x-axis or on the y-axis.

Answer 6

Every S.H.M has an initial phase angle.

Answer 7

-- Amplitude

-- Frequency

Answer 8

Requirement of mean position: It means there should be a mean position available in the system. It is the position where net force on the body is zero.

Restoring force/ restoring torque: If we observe the definition the motion should be to and fro. For to and fro motion we need a force that always bring the particle towards mean position. Such a force is called restoring force(and restoring torque in case of angular oscillations). For example, in the case of simple pendulum gravitational force acts as restoring force. In case of oscillation of a spring block system spring force acts as a restoring force.

Variable force: Only a variable force can result in oscillations. A constant force can never result in oscillations. For example, spring block system oscillates and in this case, spring force provides the restoring force which is a variable force.

Stable equilibrium position: Point no. 1 says we need a mean position. The another name of the mean position is equilibrium position. There are three types of equilibrium namely stable, unstable and neutral equilibrium(although we have a metastable equilibrium as well). Only a position of stable equilibrium position(mean position ) would result in oscillations.

External disturbance: When the particle is initially in mean position the net force acting on it is zero. So by itself, it will not start oscillating. Some external disturbance is initially required for it to start oscillating.