Three simple harmonic motions of equal amplitude A and equal time periods in the same direction combine. The phase of the second motion is 60° ahead of the first and the phase of the third motion is 60° ahead of the second. Find the amplitude of the resultant motion.
Answers
Answer ⇒ The amplitude of the resultant S.H.M. is 2A.
Explanation ⇒ Refer to the attachment for this question.
Let us first see the two S.H.M.
|R|² = A² + A² + 2A²Cos60
∴ |R|² = 2A² + 2A²Cos60
∴ |R|² = 2A² + A²
∴ |R| = √3A
Now, this S.H.M. will makes an angle of 30° with each S.H.M. of two parts which we have taken.
Thus, It will make 90° angle with the third S.H.M.
∴ |R|² = 3A² + A² + 2(3A²)(A²)Cos90
∴ |R|² = 4A²
∴ |R| = 2A
Hence, the amplitude of the resultant S.H.M. is 2A.
Hope it helps.
Answer:
Answer ⇒ The amplitude of the resultant S.H.M. is 2A.
Explanation ⇒ Refer to the attachment for this question.
Let us first see the two S.H.M.
|R|² = A² + A² + 2A²Cos60
∴ |R|² = 2A² + 2A²Cos60
∴ |R|² = 2A² + A²
∴ |R| = √3A
Now, this S.H.M. will makes an angle of 30° with each S.H.M. of two parts which we have taken.
Thus, It will make 90° angle with the third S.H.M.
∴ |R|² = 3A² + A² + 2(3A²)(A²)Cos90
∴ |R|² = 4A²
∴ |R| = 2A
Hence, the amplitude of the resultant S.H.M. is 2A.
Hope it helps.