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.The driving frequency $\omega$_d that will produce the largest amplitude response in the mass's oscillation is A)12.2 rad/s. B)1.625 rad/s. C)148 rad/s. D)24.6 rad/s. E)64.3 rad/s.

Question

Quizplus · Accepted Answer

The driving frequency that will produce the largest amplitude response in the mass's oscillation is the natural frequency of the system, which can be calculated using the formula $\omega_0 = \sqrt{\frac{k}{m}}$, where $k$ is the spring constant and $m$ is the mass. Substituting the given values, $\omega_0 = \sqrt{\frac{375}{2.54}} \approx 12.2$ rad/s.

A Mass M = 2 ω\omegaω dt),where Fd = 75 ω\omegaω d That Will Produce the Largest Amplitude Response in the Wall

A Mass M = 2 $\omega$ _dt),where F_d = 75 $\omega$ _d That Will Produce the Largest Amplitude Response in the Wall