The simple harmonic motion of a particle is given by y = 3 sing co t + 4 cos co t. Which one of the following is the amplitude of such motion?

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Q: 37 (NDA-II/2008)
The simple harmonic motion of a particle is given by y = 3 sing co t + 4 cos co t.
Which one of the following is the amplitude of such motion?

question_subject: 

Science

question_exam: 

NDA-II

stats: 

0,10,4,0,10,4,0

keywords: 

{'simple harmonic motion': [0, 0, 4, 4], 'amplitude': [1, 0, 7, 8], 'particle': [0, 2, 8, 30], 'such motion': [0, 0, 1, 0]}

The given equation for simple harmonic motion is y = 3 sin(ωt) + 4 cos(ωt). In this equation, the amplitude of the motion is the coefficient of the trigonometric functions sin(ωt) and cos(ωt). In this case, the amplitude is the coefficient of sin(ωt), which is 3. Therefore, option 1, which states that the amplitude is 1, is incorrect.

On the other hand, option 2 states that the amplitude is 5. However, this is not the correct answer. The correct amplitude for the given motion is 3, as we derived from the given equation.

Option 3 states that the amplitude is 7, which is incorrect. Option 4 states that the amplitude is 12, which is also incorrect.

In conclusion, the correct answer is option 1, with an amplitude of 3.