wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

For the given equation representing position, y=A sinωt+Asin(ωt+2π3), match the column.
Column IColumn II(A) Motion(p) Is periodic but not SHM(B) Amplitude(q) Is SHM(C) Initial phase(r) A(D) Maximum velocity(s)π3(t)ω3(u) None

A
Aq,Br,Cs,Du
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
Aq,Br,Cu,Dt
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
Ap,Br,Cu,Dr
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
Ap,Bu,cu,Dt
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A Aq,Br,Cs,Du
Given,
y=A sin ωt+A sin (ωt+2π3)
This can also be written as
y=A[sin ωt+sin (ωt+2π3)] ...(i)
Using trigonometry formula, sin C+sin D=2 sin(C+D2)cos(CD2)
Eq.(i) can be written as:
y=2A sin (ωt+π3)cos(π3)
y=2A sin (ωt+π3)cos(π3)
y=A sin(ωt+π3) ...(ii)
Comparing the above equation with y=A sin(ωt+ϕ)
we can conclude that equation (ii) represents SHM with amplitude =A, initial phase (ϕ)=π3.
Differentating Eq.(ii) w.r.t t on both sides we get,
v=dydt=ωA cos (ωt+π3)
Velocity(v) will attain maximum value when, A cos (ωt+π3)=1
vmax=ωA

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon