Which of the following describe ϕ for the SHM of Fig. 15-20 a : (a) −π < ϕ < −π/2, (b) π < ϕ < 3 π/3, (c) −3 π/2 < ϕ < −π? Figure 15-20
Which of the following describe ϕ for the SHM of Fig. 15-20 a : (a) −π < ϕ < −π/2, (b) π < ϕ < 3 π/3, (c) −3 π/2 < ϕ < −π? Figure 15-20
Which of the following describe ϕ for the SHM of Fig. 15-20a:
(a) −π < ϕ < −π/2,
(b) π < ϕ < 3 π/3,
(c) −3 π/2 < ϕ < −π?
Figure 15-20
Definition Definition Special type of oscillation where the force of restoration is directly proportional to the displacement of the object from its mean or initial position. If an object is in motion such that the acceleration of the object is directly proportional to its displacement (which helps the moving object return to its resting position) then the object is said to undergo a simple harmonic motion. An object undergoing SHM always moves like a wave.
Expert Solution & Answer
To determine
To find:
The limits which describes ∅ for SHM.
Answer to Problem 1Q
Solution:
The limits which describes ∅ for the SHM are π<∅<3π2and-π<∅<-π2.
Explanation of Solution
1) Concept:
We can use displacementof SHM to find the expression for x at t = 0.Then observing the graph, we can interpret the possible values of the phase angle.
2) Formulae:
Xt=Acos(ωt+∅)
3) Given:
The graph of x vs t is given.
4) Calculations:
Limit which describes ∅ for SHM:
We know the equation of SHM
Xt=Acos(ωt+∅)
Where A is the maximum displacement, ω is the angular velocity, t is time and ∅ is the phase difference.
At t = 0 we get,
X=Acos(∅)
From the graph, we can see that at t = 0 the value of X is negative, we know that the value of cos is negative in II and III quadrant.
So the limits are
π<∅<3π2and-π<∅<-π2
Conclusion:
We can use the equation for displacement of SHM to find the phase angle of the oscillatory motion.
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