Loaded spring in simple harmonic motion

A mass less spring suspended at a rigid support and having a heavy mass suspended at the bottom can execute simple harmonic motion under a slight disturbance.

We can derive the question for the time period of a loaded spring. The restoring force on the spring is directly proportional to the extension of the spring and the proportionality constant is called Force constant or spring constant.

The force constant of the spring is inversely proportional to its length. More than length , Les the spring constant value.

Problem and solution

a spring of certain length is divided into two parts having lengths in the ratio of 2 : 3 .What is going to be the spring constant of the longer part?

We can use the concept that spring constant of this spring is inversely proportional to the length as shown below.

Expression for the time period of a loaded spring

The force that is acting towards the mean position is the restoring force and the force acting in the opposite direction is the weight of the load that is suspended. At an equilibrium position we can equate this two forces therefore we can get time period of a loaded spring as shown.

The time period of a simple pendulum is dependent of acceleration due to gravity.But the time period of loaded spring the independent of this gravitational forces. Therefore loaded spring can be operated even in the space and vacuum where as a simple pendulum cannot be operated because of the absence of the acceleration due to gravity.

Effective spring constant when they are connected in series and in parallel

When the springs are connected in parallel the force applied on the combination will be shared across them but each of them will have the similar kind of extension.

When the springs are connected in series the force acting on both of them is going to be the same but each of them is going to extend differently basing on the nature.

Using this concept we can derive a question for the effective spring constant when they are connected in series and in parallel as shown below.

Problem and solution

Find the effective spring constant of the system as shown below?

We can solve the problem simply by applying the concept that the effective spring constant is decreasing when they are connected in series and it is increasing when there are connected in parallel as per the derivation that is made in the previous diagram.