The figure given below depicts two circular motions. The radius of the circle, the period of revolution, the initial position, and the sense of revolution are indicated in the figures.  Equations of the x-projection of the radius vector of the rotating particle P in each case are, respectively:


 
1. \(\mathrm{x}(\mathrm{t})=\mathrm{A} \cos \left(\frac{2 \pi}{4} \mathrm{t}+\frac{\pi}{4}\right)\text{ and }\mathrm{x}(\mathrm{t})=\mathrm{B} \cos \left(\frac{\pi}{15} \mathrm{t}-\frac{\pi}{2}\right)\)
2. \(\mathrm{x}(\mathrm{t})=\mathrm{A} \cos \left(\frac{2 \pi}{4} \mathrm{t}+\frac{\pi}{4}\right)\text{ and }\mathrm{x}(\mathrm{t})=\mathrm{B} \sin \left(\frac{\pi}{15} \mathrm{t}-\frac{\pi}{2}\right)\)
3. \(\mathrm{x}(\mathrm{t})=\mathrm{A} \cos \left(\frac{2 \pi}{4} \mathrm{t}+\frac{\pi}{4}\right)\text{ and }\mathrm{x}(\mathrm{t})=\mathrm{B} \cos \left(\frac{\pi}{15} \mathrm{t}-\frac{\pi}{4}\right)\)
4. \(\mathrm{x}(\mathrm{t})=\mathrm{A} \sin \left(\frac{2 \pi}{4} \mathrm{t}+\frac{\pi}{4}\right)\text{ and }\mathrm{x}(\mathrm{t})=\mathrm{B} \cos \left(\frac{\pi}{15} \mathrm{t}-\frac{\pi}{2}\right)\)
Subtopic:  Linear SHM |
From NCERT
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh

A body oscillates with SHM according to the equation (in SI units), x = 5 cos [2π t + π/4]. At t = 1.5 s, acceleration of the body will be:

1. \(140 \mathrm{~cm} / \mathrm{s}^2 \) 2. \(160 \mathrm{~m} / \mathrm{s}^2 \)
3. \(140 \mathrm{~m} / \mathrm{s}^2 \) 4. \(14 \mathrm{~m} / \mathrm{s}^2\)
Subtopic:  Linear SHM |
 57%
From NCERT
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh