NCERT Class 11 Physics Solutions: Chapter 14 – Oscillations-Part 9

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Question 14.13:

Figure (a) shows a spring of force constant clamped rigidly at one end and a mass m attached to its free end. A force F applied at the free end stretches the spring. Figure (b) shows the same spring with both ends free and attached to a mass at either end. Each end of the spring in Figure(b) is stretched by the same force .

Figure (a) shows a spring of force constant k clamped rigidl …

Spring of Force Constant K Clamped at One End

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What is the maximum extension of the spring in the two cases?

For the one block system:

When a force F, is applied to the free end of the spring, an extension l, is produced. For the maximum extension, it can be written as:

Where,

is the spring constant

Hence, the maximum extension produced in the spring,

For the two block system:

The displacement produced in this case is:

Net force,

For the one block system:

For mass of the block, force is written as:

Where, is the displacement of the block in time

It is negative because the direction of elastic force is opposite to the direction of displacement.

Where,

Where,

is angular frequency of the oscillation

Time period of the oscillation,

For the two block system:

It is negative because the direction of elastic force is opposite to the direction of displacement.

Where,

Angular frequency,

Time period,