If y = 6 Sin2t + 8Sin 2t represents the simple harmonic motion. Find amplitude and
initial phase of SHM.
Answers
Answer:
Displacement equation is given as Y=0.08sin(3πt+
4
π
)
On comparing with Y=Asin(wt+π)
We get, w=3π and ϕ=
4
π
Time period T=
T
2π
=
3π
2π
=
3
2
s
Initial phase ϕ=
4
π
At t=
36
7
s, Y=0.08sin(3π×
36
7
+
4
π
)=0.08 sin(5π/6)
⟹ Y=0.08×0.5=0.04 m
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Answer:
The amplitude of given simple harmonic motion (SHM) is 14 and initial phase is 0.
Explanation:
Simple Harmonic Motion (SHM)
- Simple harmonic motion is the motion in which the restoring force acts towards some mean position and is directly proportional to the displacement of the particle.
- In SHM displacement of particle is sinusoidal function of time.
- SHM is a type of periodic motion.
- This motion is represented by sine or cosine function of time.
The equation of simple harmonic motion is given by
y = A sin (ωt + φ) (1)
where y is the displacement of the particle, A is the amplitude of wave, ω is the angular frequency of the wave, t is time and φ is the initial phase.
Amplitude of the motion is the maximum displacement it covers.
Initial phase is the constant and describes the position of particle at t = 0 s.
The given equation is
y = 6 sin 2t + 8 sin 2t
Or y = 14 sin 2t (2)
By comparing the equation (2) with (1), amplitude A = 14 and initial phase φ = 0.