A mass M = 2.54 kg is attached to a wall with a spring with spring constant k = 375 N/m.The mass slides on a frictionless floor.The spring and mass are immersed in a fluid with damping coefficient 8.25 kg/s.An external sinusoidal horizontal force F(t)= F_dcos($\omega$_dt),where F_d = 75.4 N,is applied to the mass,causing the mass to oscillate back and forth.You may neglect the mass of the spring.What is the largest amplitude response in the mass's oscillation this driving force can produce? A)0.76 m B)0.52 m C)1.00 m D)0.89 m E)1.23 m

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Quizplus · Accepted Answer

The largest amplitude response in the mass's oscillation can be calculated using the formula for the amplitude of a driven harmonic oscillator, which is $A = \frac{F_0}{\sqrt{(k - M\omega^2)^2 + (b\omega)^2}}$, where $F_0$ is the driving force amplitude, $k$ is the spring constant, $M$ is the mass, $\omega$ is the driving angular frequency, and $b$ is the damping coefficient. Given that we do not have the driving angular frequency, we cannot directly calculate the amplitude. However, the question seems to be theoretical, aiming to test understanding of the system's dynamics rather than requiring a specific calculation with $\omega$. The correct answer must be inferred based on the information provided or prior knowledge about such systems. Since we cannot calculate without $\omega$, and given the provided choices, the answer provided here is based on the assumption that the question intended to test conceptual understanding rather than involve detailed calculation with all necessary parameters.

A Mass M = 2 ω\omegaω dt),where Fd = 75

A Mass M = 2 $\omega$ _dt),where F_d = 75