To determine the amplitude of vibration for a harmonic oscillator, we need to use the relationship between the mass, spring constant, and velocity of the system.
In a harmonic oscillator, the amplitude (A) is related to the mass (m), spring constant (k), and velocity (v) through the following equation:
A = v / (ω √(m/k))
where ω is the angular frequency given by ω = √(k/m).
Let's calculate the amplitude using the given values:
Mass (m) = 4.5 kg Spring constant (k) = 20 N/m Velocity (v) = 5 m/s
First, we calculate the angular frequency:
ω = √(k/m) = √(20 N/m / 4.5 kg) ≈ 2.108 rad/s
Now, we can substitute the values into the amplitude equation:
A = 5 m/s / (2.108 rad/s √(4.5 kg / 20 N/m))
A = 5 m/s / (2.108 rad/s √(0.225 kg/N))
A = 5 m/s / (2.108 rad/s * 0.474 N/kg)
A ≈ 5 m/s / 1.000
A ≈ 5 m
Therefore, the amplitude of the vibration in this harmonic oscillator system is approximately 5 meters.