Answer :
The amplitude of forced motion (X) of the weight suspended from the spring of stiffness 3700 N/m is approximately 0.072 m. So the correct option is d.
To find the amplitude of forced motion of the weight (X), we can use the formula for the amplitude of forced oscillation in a harmonic system:
X = F0 / m / (ω² - ω0²)
where:
F0 = Amplitude of the harmonic force (given as 67 N)
m = Mass of the weight (calculate as weight / gravitational acceleration)
ω = Angular frequency of the forced oscillation (calculate as 2π * frequency)
ω0 = Angular frequency of the spring-mass system (calculate as √(stiffness / mass))
Weight = 43 N
Stiffness = 3700 N/m
Amplitude of harmonic force (F0) = 67 N
Frequency = 4 Hz
1. Calculate the mass (m) of the weight:
m = Weight / gravitational acceleration = 43 N / 9.81 m/s² ≈ 4.38 kg
2. Calculate the angular frequency of the forced oscillation (ω):
ω = 2π * Frequency = 2π * 4 Hz ≈ 25.13 rad/s
3. Calculate the angular frequency of the spring-mass system (ω0):
ω0 = √(Stiffness / mass) = √(3700 N/m / 4.38 kg) ≈ 15.09 rad/s
4. Calculate the amplitude of forced motion (X):
X = F0 / m / (ωv- ω0²) = 67 N / 4.38 kg / (25.13² - 15.09²) ≈ 0.072 m
The amplitude of forced motion of the weight (X) is approximately 0.072 m (option d).
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