The initial phase angle for is
(A)
(B)
(C)
(D)
Answer
Verified
450.9k+ views
Hint: We are given with an equation and are asked to find the initial phase angle for the same. Thus, we will firstly evaluate the equation at time . Then, we will use some basic trigonometric ideas to manipulate the evaluated value and then come up with an answer.
Complete Step By Step Solution
Here, The given equation is,
Now, For the initial value, we take time
Taking here, we get
We know,
And
Thus, we get
Further, we get
Now,
Further, we get
Where, is the amplitude of the motion.
Now,
As per the generic equation of such motion,
For time ,
Then, we get
Thus, we get
Thus,
Thus,
Thus,
Hence, we get
Hence, the correct option is (A).
Note
We have converted the sine function to a tangent one as all the given options are in the same format. We used basic trigonometry for conversion. One should not confuse it to be a given parameter.
Complete Step By Step Solution
Here, The given equation is,
Now, For the initial value, we take time
Taking here, we get
We know,
Thus, we get
Further, we get
Now,
Further, we get
Where,
Now,
As per the generic equation of such motion,
For time
Then, we get
Thus, we get
Thus,
Thus,
Thus,
Hence, we get
Hence, the correct option is (A).
Note
We have converted the sine function to a tangent one as all the given options are in the same format. We used basic trigonometry for conversion. One should not confuse it to be a given parameter.
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