1. In the periodic function x = A sin(ωt + φ), what does φ represent?
A.
Amplitude
B.
Angular frequency
C.
Initial phase
D.
Time period
Correct Answer:
Initial phase
Explanation:
The constant φ is called the initial phase because it gives the phase of the oscillator at time t = 0.
2. What is the phase of the function x = A sin(ωt + φ) at t = 0?
A.
0
B.
φ
C.
ω
D.
A
Correct Answer:
φ
Explanation:
Substituting t = 0 into ωt + φ gives the phase φ.
3. For the function x = A cos(ωt), the initial phase is:
A.
0
B.
π/2
C.
π
D.
2π
Correct Answer:
0
Explanation:
The function can be written as x = A cos(ωt + 0), so its initial phase is zero.
4. Which expression represents a periodic function with an initial phase of π/2?
A.
x = A sin(ωt)
B.
x = A sin(ωt + π/2)
C.
x = A sin(ωt + π)
D.
x = A sin(ωt + 2π)
Correct Answer:
x = A sin(ωt + π/2)
Explanation:
In x = A sin(ωt + φ), the constant added to ωt is the initial phase. Here it is π/2.
5. If x = A sin(ωt + π), what is the initial phase?
A.
0
B.
π/2
C.
π
D.
2π
Correct Answer:
π
Explanation:
Comparing the expression with x = A sin(ωt + φ), the initial phase is φ = π.
6. Which function has an initial phase of π/4?
A.
x = A cos(ωt + π/4)
B.
x = A sin(ωt + π/4)
C.
x = A sin(ωt - π/4)
D.
x = A sin(ωt)
Correct Answer:
x = A sin(ωt + π/4)
Explanation:
The initial phase is the constant phase added to ωt. In this expression, it is +π/4.
7. The functions x = A sin(ωt + 2π) and x = A sin(ωt) have:
A.
Different amplitudes
B.
Different angular frequencies
C.
The same initial phase effectively
D.
Different time variables
Correct Answer:
The same initial phase effectively
Explanation:
Phases differing by 2π represent the same phase position in a periodic function, so 2π is equivalent to zero initial phase.
8. If a periodic function is written as x = A sin(ωt - π/3), its initial phase is:
A.
π/3
B.
-π/3
C.
2π/3
D.
3π
Correct Answer:
-π/3
Explanation:
Comparing with x = A sin(ωt + φ), the phase constant is φ = -π/3.
9. At t = 0, the phase of x = A cos(ωt + π/6) is:
A.
0
B.
π/6
C.
ω
D.
A
Correct Answer:
π/6
Explanation:
At t = 0, the phase ωt + π/6 becomes π/6, which is the initial phase.
10. If the initial phase of x = A sin(ωt + φ) is zero, which equation is correct?
A.
x = A sin(ωt)
B.
x = A sin(ωt + π/2)
C.
x = A sin(ωt + π)
D.
x = A sin(ωt - π/2)
Correct Answer:
x = A sin(ωt)
Explanation:
Zero initial phase means φ = 0, so the function becomes x = A sin(ωt).
Short questions are currently unavailable for this page.