NCERT Class 11 Physics Solutions: Chapter 14 – Oscillations-Part 7

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Question 14.11:

Figures correspond to two circular motions. The radius of the circle, the period of revolution, the initial position, and the sense of revolution (i.e. clockwise or anti-clockwise) are indicated on each figure.

Figures correspond to two circular motions. The radius of th …

Figure Shown the Two Circular Motions

Obtain the corresponding simple harmonic motions of the x-projection of the radius vector of the revolving particle in each case.

Answer:

For Figure

Time period,

Amplitude,

At time, , the radius vector makes an angle with the positive , i.e.,

Phase angle

Therefore, the equation of simple harmonic motion for the projection of , at time , is given by the displacement equation:

For Figure

Time period,

Amplitude,

At time, makes an anglewith the x-axis, in the anticlockwise direction.

Hence, phase angle,

Therefore, the equation of simple harmonic motion for the projection of at time is given as: