NCERT Class 11 Physics Solutions: Chapter 14 – Oscillations-Part 4

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Question 14.6:

Which of the following relationships between the acceleration and the displacement of a particle involve simple harmonic motion?

Answer:

Explanation:

A motion represents simple harmonic motion if it is governed by the force law:

Where,

Is the force

Is the mass (a constant for a body)

Is the displacement

Is the acceleration

Is a constant

Among the given equations, only equation is written in the above form with

Hence, this relation represents simple harmonic motion.

Question 14.7:

The motion of a particle executing simple harmonic motion is described by the displacement function,

If the initial position of the particle is and its initial velocity is , what are its amplitude and initial phase angle? The angular frequency of the particle is If instead of the cosine function, we choose the sine function to describe the SHM: what are the amplitude and initial phase of the particle with the above initial conditions.

Answer:

Initially, at

Displacement,

Initial velocity,

Angular frequency,

It is given that:

Squaring and adding equations, we get:

Dividing equation, by equation we get:

SHM is given as:

Putting the given values in this equation, we get:

Velocity,

Substituting the given values, we get:

Squaring and adding equations we get:

Dividing equation by equation, we get: