Get 2 FREE Instant-Explanations on Filo with code FILOAPP

The displacement of a particle varies with time according to t

Question

The displacement of a particle varies with time according to the relation $y = a s inω t + b cos ω t .$

The motion is oscillatory but not SHM.

The motion is SHM with amplitude a + b.

The motion is SHM with amplitude

a^{2} + b^{2}

The motion is SHM with amplitude

a^{2} + b^{2}

Views: 1,140 students

Found 7 tutors discussing this question

Evelyn Discussed

The displacement of a particle varies with time according to the relation

y = a s inω t + b cos ω t .

14 mins ago

Discuss this question LIVE

14 mins ago

Text solutionVerified

Given

x = a s inω t + b cos ω t

.......(i)

Let

a = A cos ϕ

........(ii)

and

b A s in ϕ

..........(iii)

Squaring adding (ii) and (iii), we get

a^{2} + b^{2} = A^{2} co s^{2} ϕ + A^{2} s i n^{2} ϕ = A^{2}

Eq.(i) can be written as

x = A cos ϕ s inω t + A s in ϕ cos ω t = A s in (ω t + ϕ)

It is equation of SHM with amplitude

A = a^{2} + b^{2}

Was this solution helpful?

152

Report

One destination to cover all your homework and assignment needs

Learn Practice Revision Succeed

Instant 1:1 help, 24x7

60, 000+ Expert tutors

Textbook solutions

Big idea maths, McGraw-Hill Education etc

Essay review

Get expert feedback on your essay

Schedule classes

High dosage tutoring from Dedicated 3 experts

Trusted by 4 million+ students

Stuck on the question or explanation?

Connect with our physics tutors online and get step by step solution of this question.

231 students are taking LIVE classes

Question Text	The displacement of a particle varies with time according to the relation $y = a s inω t + b cos ω t .$
Answer Type	Text solution:1
Upvotes	152