For the simple harmonic motion described by the trigonometric function, find the least positive value of t for which

Question

For the simple harmonic motion described by the trigonometric function, find the least positive value of t for which  ​  ​

Quizplus · Accepted Answer

The given function can be written as

y = 2sin(3t + π/4) + 5

We need to find the least positive value of t for which y = 6, i.e.,

2sin(3t + π/4) + 5 = 6

2sin(3t + π/4) = 1

sin(3t + π/4) = 1/2

We know that sin(π/6) = 1/2

So,

3t + π/4 = π/6 + 2kπ or 3t + π/4 = 5π/6 + 2kπ

where k is an integer.

Solving for t, we get

t = (π/6 - π/4)/3 + (2kπ/3) or t = (5π/6 - π/4)/3 + (2kπ/3)

t = π/36 + (2kπ/3) or t = 7π/36 + (2kπ/3)

The least positive value of t will be the smallest positive root of these equations.

Substituting k = 0, we get t = π/36 and t = 7π/36 are the smallest positive roots.

Of these, π/36 is the smallest positive value of t.

Hence, the answer is B) 11eacce6_1d08_9f61_9f49_0790588ec1bc_TB7896_11.

For the Simple Harmonic Motion Described by the Trigonometric Function