Respuesta :
Answer:
A) Φ = 0 , B) T = 7.76 s
Explanation:
A) to find the value of the phase constant replace the value
0 = a sin (b (0- 0) + Φ)
0 = sin Φ
Φ = sin⁻¹ 0
Φ = 0
B) the period is defined by time or when the movement begins to repeat itself
So that the sine function is repeated when the angle passes 2pi
b (x- ct) = 2pi
If we are at a fixed point x = 0
b c t = 2pi
t = 2π / bc
Let's calculate
T = 2π / (33.05 245)
T = 7.76 s
Answer:
A. Φi = 0
B. Simple harmonic period, T = 0.0445s
Explanation:
Parameters given:
a = 0.00580 m
b = 33.05 m-1
c = 245 m/s
A. At time t = 0 and point x = 0, f(x, t) = 0. Hence, the string is not moving at all. It is static and in its start position.
f(x, t) = asin[b(x - ct) + Φi]
f(0,0) = asin[b(0 - 0) + Φi] = 0
asin[b(0) - Φi] = 0
asin[Φi] = 0
sinΦi = 0
Φi = sin-1(0)
Φi = 0
B. By comparing the given function with the general wave function,
f(x, t) = Asin(kx - ωt + Φ) ; f(x, t) = asin(bx - bct + Φi)
a = A (amplitude of the wave)
b = k (wave number)
bc = ω (angular frequency)
The period of the simple harmonic motion can then be found using:
T = 2π/ω
=> T = 2π/bc
T = 2π/(33×245)
T = 0.0445 s
The simple harmonic period is 0.0445s
