Oscillations due to a Spring

Introduction

In physics, an oscillating system is a physical system that undergoes a periodic change in state, just like when you swing on a swing or when a spring oscillates. The system repeats itself through a repeating pattern.

In this case, a spring oscillates by moving outward and then back inward. The frequency refers to how many times the system oscillates in a given amount of time. The relaxation period is the time it takes for the spring to oscillate backward after it has reached the end of its range of motion.

This article is about oscillations, their meaning, types, and equations of oscillation due to spring.

Oscillation

Oscillation is defined as a process in which a thing periodically repeats itself over time. For example, if you were to describe something as oscillating between two values, it would mean that the quantity was going back and forth between any given value and its average. In mechanical systems oscillation refers to circular or elliptical motion – such as oscillations of a pendulum around the equilibrium position. Oscillate means to swing back and forth like a pendulum.

Vibration is the term used to describe the mechanical oscillations of an object. Conversely, oscillations also occur in dynamic systems or, more accurately, in every field of science. Ever hear your heart thumping in your chest? That’s an example of vibration, and they can even be felt internally as well. Another example of vibrations in our environment and how it reacts to external sources. Oscillators are objects that show motion around an equilibrium point.

Oscillatory Motion 

Oscillatory motion is the kind of circular motion that goes back and forth around one point in space. If a pendulum is swinging up and down, it’s an example of oscillatory motion. In reality, though, all 3-dimensional bodies will eventually come to rest because of forces like friction or air pressure. You can keep oscillation, however, by keeping the time between swings roughly equal to an external force. 

For example:  

• A seesaw needs someone using their gravity to hold it in the air or it won’t stay balanced between the kids riding it  

• A child pushing on a swing holds its position when the right amount of force is applied

Types of Oscillations

Under Damped Oscillations

An under-damped system returns to an equilibrium point more quickly than an overdamped or critically damped system. An under-damped sine wave oscillates rapidly, while all other graphs have slower oscillations. As the damping reduces the amount of energy dissipated in a system, an under-damped represents (both algebraically and geometrically) the smallest energy dissipation compared to other damping systems such as an overdamped system.

Critically Damped Oscillations

Critical damping refers to an oscillation with damping such that the force available is just sufficient to bring the system into equilibrium in the first application, and that any subsequent applications of force will not cause the system to move. Critical damping is the kind of damping in which the damping constant is equal to one and occurs when oscillations come back to their original position quickly. Critical damping is required for a system to not oscillate about its equilibrium point. In critical damping, the amount of necessary damping is finely proportioned to keep the oscillation within range with no more wobbling back and forth.

Over Damped Oscillations

When the damping value is greater than one, we call it overdamping. This can be understood from mathematics as when damping is high (depending on the frequency, of course); the oscillations approach equilibrium very quickly and hence, do not have time to bounce back and forth across equilibrium. This means that there will be a lot fewer oscillations in this case compared to areas where damping has yet to be applied.

Undamped Oscillations

An undamped and oscillating signal is any signal that does not experience interference from external resistance. This means that an undamped signal will continue to oscillate with constant amplitude and frequency until a damping factor or external force causes it to lose energy.

The current under the influence of no opposing force is a simple illustration of an undamped system. Under these circumstances, the current oscillates to and fro in a self-perpetuating manner with no limit to the number of cycles it may undergo. If the supply voltage is above the normal operating value, the cycle begins on alternate half-cycles and completes itself at intervals which tend to decrease as the oscillations produced become more vigorous in amplitude. The rate of this change constitutes the damping factor that measures how rapidly damped is an undamped vibration.

Oscillations due to a Spring

Consider a block that is pulled on one side and then released, causing it to oscillate back and forth around its mean position. The block is  moving without friction on a surface that also does not contribute to resistance. This means that a block moving in this way will remain at the same velocity until it comes into contact with another object.

F(x) = -kx, where, F is force, x is the displacement, m is the mass and omega is angular frequency.

• It is known that k is the spring constant of spring and its value is governed by the elasticity of the spring

• The above expression is the same as the force law for SHM and therefore the system executes a simple harmonic motion

• w = √k/m

• T = 2√m/k where T is the period

Conclusion

Spring is a device that stores potential energy and when it is stretched or compressed, it stores the energy. The spring will then release the energy when it oscillates. The amount of energy the spring releases depends on how hard the spring is compressed. Energy is conserved when a spring oscillates. This article is about oscillations, their meaning, types, and equations of oscillation due to spring.