Answer:
A: The frequency of the vibration is 1.3329 Hz
B: The total energy of the vibration is 18.39375 J
Explanation:
The force of the man his weight causes the raft to sink, and that causes the water to put a larger upward force on the raft. This extra force is a restoring force, because it is in the opposite direction of the force put on the raft by the man. Then when the man steps off, the restoring force pushes upward on the raft, and thus the raft – water system acts like a spring, with a spring constant found as follows:
k= F/x = ((75 kg) * (9.81 m/s²))/(5*10^-2 m) = 14715 N/m
The frequency of the vibration is determined by the spring constant (k) and the mass of the raft (210kg).
fn = 1/2π * √(k/m) = 1/2π * √(14715 / 210) = <u>1.3329 Hz</u>
<u>The frequency of the vibration is 1.3329 Hz</u>
<u />
<u>b) </u>
Since the gravitational potential energy can be ignored, the total energy will be :
Etot = 1/2 k* A² = 1/2 * (14715 )*(0.05)² = 18.39375 J
<u>The total energy of the vibration is 18.39375 J</u>
(a) 
The relationship between frequency and wavelength of an electromagnetic wave is given by

where
is the speed of light
is the frequency
is the wavelength
In this problem, we are considering light with wavelength of

Substituting into the equation and re-arranging it, we can find the corresponding frequency:

(b) 
The period of a wave is equal to the reciprocal of the frequency:

And using
as we found in the previous part, we can find the period of this wave:

Solve for acceleration:
<em>a</em> = (21.4 m/s - 33.8 m/s) / (4.7 s)
<em>a</em> ≈ -2.6 m/s²
Solve for force:
<em>F</em> = (1400 kg) <em>a</em> ≈ -3700 N
The minus sign tells you the force points in the opposite direction of the car's motion. Its magnitude is always positive, so <em>F</em> = 3700 N.