This is a practice problem for physics. I really need help coz I tried it twice

Question

This is a practice problem for physics.

I really need help coz I tried it twice but failed.

Below is question:

Two sinusoid signals, described by 1 = cos( + ) and 2 = cos + , enter the same region, creating a resulting oscillation shown in the picture below. Signal 1() has a magnitude of 4.15 cm and its initial phase constant is 2.83 rad.

Question 1: What is the magnitude of signal 2 (answer in cm)?

Question 10: What is the initial phase constant of signal 2? Give your answer in radians as a number between 0 and 2pi.

Figure:

For question 1I got 0.85cm and 1.20cm.

For question 2, I got 2.82 and 3.14 rad.

They are both wrong.

Explanation / Answer

As s = s1 + s2

s2 = s-s1

s1 = 4.15 cos(wt + 2.83) = 4.15 < (pi/2 - 2.83) = 4.15<-1.26 rad

= 4.15 < 72.2 deg

If you look at the wave

it starts from 0.15 sec. And time period is (2-0.15) = 1.85 sec

initial phase ange is = 2 pi 0.15 / 1.85 = 0.51 rad

so,

s = 5sin(wt-0.51) = 5 < 0.51rad

= 5 < 29.22 deg

s2 = s-s1

= 5<29.22 - 4.15<72.2

= 3.44 < -26 deg

= 3.44 cm < -26 + 360

= 3.44cm < 334 deg

= 3.44 cm < 5.83 rad or 3.44 cm < 1.855 pi rad

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