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

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Question 14.16:

Answer the following questions:

(a) Time period of a particle in SHM depends on the force constant k and mass m of the particle:

. A simple pendulum executes SHM approximately. Why then is the time period of a pendulum independent of the mass of the pendulum?

(b) The motion of a simple pendulum is approximately simple harmonic for small angle oscillations. For larger angles of oscillation, a more involved analysis shows that is greater than Think of a qualitative argument to appreciate this result.

(c) A man with a wristwatch on his hand falls from the top of a tower. Does the watch give correct time during the free fall?

(d) What is the frequency of oscillation of a simple pendulum mounted in a cabin that is freely falling under gravity?

Answer:

the soring mass system is showing in figure.

Figure Shown the Soring Mass System

Explanation:

The time period of a simple pendulum,

For a simple pendulum, is expressed in terms of mass as:

Hence, the time period of a simple pendulum is independent of the mass of the bob.

Explanation:

In the case of a simple pendulum, the restoring force acting on the bob of the pendulum is given as:

Where,

Restoring force

Mass of the bob

Acceleration due to gravity

Angle of displacement

For small

For large is greater than

This decreases the effective value of

Hence, the time period increases as:

Where, is the length of the simple pendulum.

Explanation:

The time shown by the wristwatch of a man falling from the top of a tower is not affected by the fall. Since a wristwatch does not work on the principle of a simple pendulum, it is not affected by the acceleration due to gravity during free fall. Its working depends on spring action.

Explanation:

When a simple pendulum mounted in a cabin falls freely under gravity, its acceleration is zero. Hence, the frequency of oscillation of this simple pendulum is zero.