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Simple Harmonic Motion (SHM) is an intriguing type of movement or motion. It is often used in the oscillating movement or motion of objects. The SHM is frequently observed in spring. Springs have inherent “spring constants or force constant” which define their stiffness. Hooke’s law is a well – known law which explains the SHM and gives a formula for the applied force using the spring constant or force constant.
Force Constant
In physics, a force constant is another term which is used for a spring constant. Force constant is as defined by Hooke’s law. More precisely, it is a constant of proportionality. The force constant k is related to the stiffness (or rigidity) of a system, the larger the force constant, the greater the force restored and the rigid the system. Newton per meter (N/m) is the unit of k. For example, if we stretch a string, k is directly related to the Young’s modulus of elasticity.
Hooke’s Law
Hooke’s law is one of the important principles of physics. The concept was given by British physicist Robert Hooke. He developed the principle in the 17th century for better innovations and inventions in the field of mechanics. This principle acts basically on the forces of the spring and its elasticity. Hooke’s law demonstrates the knowledge of mechanics that was effectively used in the invention of many electronic devices. This law is still relevant because it is efficient enough to be used in the manufacture of technical devices even now.
According to Hooke’s law, the force needed to compress or expand a spring is proportional to the stretched length. When the spring is pulled, Newton’s third law of motion states that it will return with a restoring force. This restoring force obeys Hooke’s Law, which relates spring force to the spring force constant.
Therefore, from the Hooke’s law, the spring force is given as
Spring Force=Spring Constant × Displacement
F=-K×X
The negative sign shows the direction of reaction force is in the opposite direction.
F = spring force
K = spring constant or force constant (Nm-¹)
X = displacement of spring from equilibrium position
Formula for force constant
From Hooke’s law, we have
F=-K×X
Therefore, force constant is given as
K= -FX
Dimensional formula for Force Constant
As we know,
K= -F/X
Dimensional formula of F = [MLT-2]
Dimensional formula of X = [L]
Therefore, the dimensional formula for force constant is K=MLT-²L
K=[MT-²]
Oscillation Motion
Oscillation motion is generally defined as the repetition of a certain action or movement (motion). A body has an oscillation motion when it repeatedly moves from its starting point to an ending point within a given time frame. Vibrations can be observed in mechanical systems and dynamic systems. Once started in oscillation motion, the desired state of a body is when it continues this “vibratory motion” indefinitely without stopping except when interrupted by an external force. However, this is not feasible because of the friction as an influencing factor and because of the friction, the object eventually slows its motion to a standstill.
When an object repeatedly moves across a point, then the object movement is an oscillation motion. In a complete vacuum, the ideal state can be achieved because there is no air to stop the object in the friction of the oscillation motion.
Simple Harmonic Motion (SHM)
The motion of a body moving back and forth along a straight line about a mean position is called simple harmonic motion. A pendulum executes a simple harmonic motion. It oscillates back and forth about its centre position where the string and bob move. These motions of the pendulum are called oscillation motion, that shows simple harmonic motion.
A simple harmonic motion can be defined as an oscillatory motion where the acceleration of a particle at any point is proportional to the displacement from the mean position. Simple harmonic motion is a special case of oscillating motion.
Periodic Motion
A motion which repeats itself at an equal interval of time is considered as a periodic motion. Examples of periodic motion are a tuning fork or the motion of a pendulum. If we analyse the movement or motion of a pendulum, we will conclude that the pendulum only passes through the mean position after a certain interval of time. We can also classify the pendulum motion as oscillation motion. An oscillation motion is a motion or movement where the body moves to and fro in a certain position. Therefore, an oscillation motion can be periodic, but is not necessary.
Conclusion
In physics, a force constant is another term which is used for a spring constant. Force constant is as defined by Hooke’s law.
According to Hooke’s law, the force needed to compress or expand a spring is proportional to the stretched length.
From the Hooke’s law, the spring force is given as
Spring Force=Spring Constant ×Displacement
F=-K×X
force constant is given as
K= -F/X
Oscillation motion is generally defined as the repetition of a certain action or movement (motion).
The motion of a body moving back and forth along a straight line about a mean position is called simple harmonic motion.
A motion which repeats itself at an equal interval of time is considered as a periodic motion.
