A particle is subjected to two SHMs, X1=A1 sin ωt and X2=A2 sin ωt+π4. The resultant SHM will have an amplitude of:

A
$\frac{(A_{1} + A_{2})}{2}$
B
$\sqrt{A_{1}^{2} + A_{2}^{2}}$
C
$\sqrt{A_{1}^{2} + A_{2}^{2} + \sqrt{2} A_{1} A_{2}}$
D
$\sqrt{\frac{A_{1}^{2} + A_{2}^{2}}{2}}$

Solution:

Resultant amplitude,
$A \sqrt{A_{1}^{2} + A_{2}^{2} + 2 A_{1} A_{2} \cos ϕ}$
Here $ϕ = \frac{π}{4}$
$\Rightarrow A = \sqrt{A_{1}^{2} + A_{2}^{2} + \sqrt{2} A_{1} A_{2}}$

Related content

Test your English Vocabulary

CUET Exam Dates 2024 – Application Form, Fees, Eligibility

CBSE Class 12 IP Answer Key 2024,Informatics Practices Paper Solution For SET 1, 2, 3, 4

CUET UG Cut Off 2024, Category, Universities and Colleges Wise Expected Cut Off

Modal Verbs

Helping Verbs

Letter To Your Friend About Your School Trip

Action Verbs

CUET 2024 – List of Colleges and Participating Universities Accepting CUET Exam Score

SRMJEEE Online Test Series – Practice Papers