At t = 0 s a mass is at a position x = 0.33A and is moving to the right. The position of the mass is described by equation . The phase angle of this motion, is
A) 0.946 rad.
B) 70.7 rad.
C) 5.34 rad.
D) 0.324 rad.
E) 5.96 rad.

Question

Quizplus · Accepted Answer

We can start with the general equation of motion for simple harmonic motion:
x = A cos(ωt + φ)
where x is the position of the mass, A is the amplitude, ω is the angular frequency, t is time, and φ is the phase angle.

We know that at t = 0 s, x = 0.33A and the mass is moving to the right, so we can conclude that φ must be positive (since the cosine function is positive for angles between 0 and π/2).

Using the given x value, we can write:
0.33A = A cos(ω(0) + φ)
0.33 = cos φ

Solving for φ, we get:
φ = cos^-1(0.33) ≈ 1.233 rad

However, we need to be careful with choosing the final answer because the possible choices are given in radians while we calculated φ in degrees. Converting φ to radians, we get:
φ ≈ 1.233 rad ≈ 5.34 rad (rounded to two decimal places)

Therefore, the best choice is C.

At T = 0 S a Mass Is at a Position