The displacement of a particle is represented by the
equation y = sin³ ⍵t. The motion is
(a) non-periodic
(b) periodic but not simple harmonic
(c) simple harmonic with period 2π/⍵
(d) simple harmonic with period π/⍵
Answers
Answered by
1
Answer:
(b) periodic but not shm
Explanation:
Given the equation of displacement of the particle, y=sin
3
ωt
We know sin3θ=3sinθ−4sin
3
θ
Hence, y=
4
(3sinωt−4sin3ωt)
⇒4
dt
dy
=3ωcosωt−4×[3ωcos3ωt]
⇒4×
dt
2
d
2
y
=−3ω
2
sinωt+12ωsin3ωt
⇒
dt
2
d
2
y
=
4
−3ω
2
sinωt+12ωsin3ωt
⇒
dt
2
d
2
y
is not proportional to y.
Hence, the motion is not SHM.
As the expression is involving sine function, hence it will be periodic.
Also sin
3
ωt=(sinωt)
3
=[sin(ωt+2π)]
3
=[sin(ωt+2π/ω)]
3
Hence, y=sin
3
ωt represents a periodic motion with period 2π/ω.
Answered by
0
Answer:
I am in class 5 so I don't know about it
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