NCERT solution Class 11 oscillations

NCERT Solutions

Class 11 Physics

Oscillations

NCERT Questions

Q. 13.1
Q. 13.2
Q. 13.3
Q. 13.4
Q. 13.5
Q. 13.6
Q. 13.7
Q. 13.8
Q. 13.9
Q. 13.10
Q. 13.11
Q. 13.12
Q. 13.13
Q. 13.14
Q. 13.15
Q. 13.16
Q. 13.17
Q. 13.18
Q. 14.7
Q. 14.8

Q. 13.13

Figure 14.30 (a) shows a spring of force constant k 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 14.30 (b) shows the same spring with both ends free and attached to a mass m at either end. Each end of the spring in Fig. 14.30(b) is stretched by the same force F.

(a) What is the maximum extension of the spring in the two cases?

(b) If the mass in Fig. (a) And the two masses in Fig. (b) Are released, what is the period of oscillation in each case?

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:

F = kl

Where, k is the spring constant

Hence, the maximum extension produced in the spring, l= (F/k)

For the two block system:

The displacement (x) produced in this case is:

x = (l/2)

Net force, F = +2 kx = 2k (l/2)

Therefore l = (F/k)

For the one block system:

For mass (m) of the block, force is written as:

F = ma = m (d²x/dt²)

Where, x is the displacement of the block in time t

Therefore, m (d²x/dt²) = -kx

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

(d²x/dt²) = - (k/m) x = - ω²x

Where ω² = (k/m)

Or ω = √ (k/m)

Where, ω = angular frequency of the oscillation

∴Time period of the oscillation, T = (2 π/ ω)

= (2 π)/ (√ (k/m)) = (2 π)/ (√ (m/k))

For the two block system:

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

(d²x/dt²) = - [2k/m] x = -ω²x

Where, angular frequency ω = (√ (2k/m))
Therefore, Time period= T = (2 π)/ (ω)

= (2 π)/ (√ (m/2k))

Video solution:

Oscillations Class 11 Physics NCERT Chapter 13 NCERT Solutions

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NCERT solutions of Oscillations Class 11 Physics - all questions of all exercises are solved. Q. No. 1, 2, 3, and so on. Complete explanation and detailed solution makes them the best videos for Class 11 Physics Oscillations NCERT solutions.