NCERT Class 11 Physics Solutions: Chapter 14 – Oscillations-Part 17

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Question 14.23:

A circular disc of mass is suspended by a wire attached to its centre. The wire is twisted by rotating the disc and released. The period of torsional oscillations is found to be The radius of the disc is . Determine the torsional spring constant of the wire. (Torsional spring constant is defined by the relation , where J is the restoring couple and the angle of twist).

Answer:

Mass of the circular disc,

Radius of the disc,

The torsional oscillations of the disc has a time period,

The moment of inertia of the disc is:

Time period,

is the torsional constant.

Hence, the torsional spring constant of the wire is

Question 14.24:

A body describes simple harmonic motion with amplitude of and a period of . Find the acceleration and velocity of the body when the displacement is .

Answer:

Amplitude,

Time period,

the velocity equation for SHM is showing in figure.

Figure Shown the Velocity Equation Fore SHM

Loading Image

Explanation:

For displacement,

Acceleration is given by:

Velocity is given by:

When the displacement of the body is its acceleration is and velocity is

Explanation:

For displacement,

Acceleration is given by:

Velocity is given by:

When the displacement of the body is , its acceleration is and velocity is

Explanation:

For displacement

Acceleration is given by:

Velocity is given by:

When the displacement of the body is , its acceleration is and velocity is