14. When two dispalcements represented by
Yo = asin(wt) and y, = b cos(at) are superimposed
the motion is :
1
a
()
(1) simple harmonic with amplitude
b
(2) simple harmonic with amplitude Va? + b2
(a+b)
(3) simple harmonic with amplitude
2
(4) not a simple harmonic
Explanation:
Answer
ω=
T
2π
=
16
2π
=
8
π
rad/s
If at t=0, particle passes through its mean position (x=Asinωt) with maximum speed its v−t equation can be written as
v=ωAcosωt
Substituting the given values, we have
2=(
8
π
)Acos(
8
π
)(2)
∴ A=
π
16
2
m=7.2 m