The bow of a 5.0E6 kg destroyer undergoes a simple vertical harmonic motion with a period of 8.0 s and amplitude of 2.0 m. The motion of the boat is recorded by a sailor. At t = 0 s, the boat is at 40 cm above the equilibrium point with an initial velocity of -25 cm/s.

a) Find the phase constant, the angular frequency, and write the equations of motion, velocity, and acceleration.

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Sadly enough, I'm having trouble finding the phase constant. I'm not sure exactly what I'm doing wrong...but due to circumstances I don't have the correct answer to look at, only one incorrect one. There are more parts to this problem but I haven't tried them yet, since I'm stuck here... So I may edit this post with another question when I can figure this one out.

I'm using x = A cos (wt + phi) , .4 = 2 cos [(-.25)(0) + phi] which gives me 1.37, the incorrect answer.

***/Edit***

d) A 90-kg sailor is standing on a scale in a bankroom near the bow. What are the maximum and minimum readings on the scale in Newtons?

- For this one would I just use a(max) = (omega^2)*A and add that to 9.81 to get the acceleration. Then multiply that by his mass? For the minimum I would just subract a(max) from gravity and do the same?

e) The ship main computer is mounted on a suspension system to protect it against vibrations and shocks. Protected by this system, a 20 Hz oscillation loses half its energy in .5 s. What are the fractional energy loss per cycle and the Q factor of the suspension system? - Absolutely no clue on this one.

***/Edit Off***

Thank you for your time and any help is greatly appreciated!

-Edge

a) Find the phase constant, the angular frequency, and write the equations of motion, velocity, and acceleration.

-----

Sadly enough, I'm having trouble finding the phase constant. I'm not sure exactly what I'm doing wrong...but due to circumstances I don't have the correct answer to look at, only one incorrect one. There are more parts to this problem but I haven't tried them yet, since I'm stuck here... So I may edit this post with another question when I can figure this one out.

I'm using x = A cos (wt + phi) , .4 = 2 cos [(-.25)(0) + phi] which gives me 1.37, the incorrect answer.

***/Edit***

d) A 90-kg sailor is standing on a scale in a bankroom near the bow. What are the maximum and minimum readings on the scale in Newtons?

- For this one would I just use a(max) = (omega^2)*A and add that to 9.81 to get the acceleration. Then multiply that by his mass? For the minimum I would just subract a(max) from gravity and do the same?

e) The ship main computer is mounted on a suspension system to protect it against vibrations and shocks. Protected by this system, a 20 Hz oscillation loses half its energy in .5 s. What are the fractional energy loss per cycle and the Q factor of the suspension system? - Absolutely no clue on this one.

***/Edit Off***

Thank you for your time and any help is greatly appreciated!

-Edge

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