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