A motor of weight m is supported by a mounting that has spring constant k. If the unbalance of the motor is equivalent to a force F=F0cos(ωt) and damping can be neglected, calculate the amplitude of the response, X0, when m = 150 kg, k = 5 MN/m, F0 = 450 kN and ω=120 rad/s. 单项选择题
登录即可查看完整答案
我们收录了全球超50000道真实原题与详细解析,现在登录,立即获得答案。

Question

A motor of weight m is supported by a mounting that has spring constant k. If the unbalance of the motor is equivalent to a force F=F0cos(ωt) and damping can be neglected, calculate the amplitude of the response, X0, when m = 150 kg, k = 5 MN/m, F0 = 450 kN and ω=120 rad/s. 单项选择题

登录即可查看完整答案

我们收录了全球超50000道真实原题与详细解析,现在登录,立即获得答案。

BlackTom AI · Accepted Answer

We start by identifying the system: a mass m attached to a mounting with spring constant k, subjected to an external force F = F0 cos(ωt) with damping neglected. For a single-degree-of-freedom mass-spring system under harmonic forcing and zero damping, the steady-state displacement has amplitude X0 given by X0 = F0 / |k − m ω^2|. This comes from balancing the inertia term m x'' with the restoring force k x in the frequency domain, yielding a dynamic stiffness of (k − m ω^2) for the forced response.

Now plug in the numbers:
- m = 150 kg
- k = 5 MN/m = 5 × 10^6 N/m
- ω = 120 rad/s
- F0 = 450 kN = 4.5 × 10^5 N

Compute the term m ω^2:
m ω^2 = 150 × (120)^2 = 150 × 14,400 = 2,160,000 N/m.

dynamic stiffness = k − m ω^2 = 5,000,000 − 2,160,000 = 2,840,000 N/m.

Finally, the amplitude X0:
X0 = F0 / |k − m ω^2| = 450,000 / 2,840,000 ≈ 0.1585 m.

Converting to centimeters: 0.1585 m × 100 cm/m ≈ 15.85 cm, which rounds to about 15.8 cm.

If any of the inputs were different (for example, including damping), the expression for X0 would include a damping term, and the amplitude would be F0 / sqrt((k − m ω^2)^2 + (c ω)^2) with c representing damping. Here, since damping is neglected, the denominator reduces to the absolute difference (k − m ω^2). Note that you should confirm the sign inside the absolute value, but only the magnitude matters for amplitude.

Regarding the answer choices: the provided data show a single numerical result for X0, and no alternative options are given to compare against. The calculation steps above lead to the numeric value in consistent units.

A motor of weight m is supported by a mounting that has spring constant k. If the unbalance of the motor is equivalent to a force F=F0cos(ωt) and damping can be neglected, calculate the amplitude of the response, X0, when m = 150 kg, k = 5 MN/m, F0 = 450 kN and ω=120 rad/s. 单项选择题

类似问题

A motor of weight m is supported by a mounting that has spring constant k. If the unbalance of the motor is equivalent to a force and damping can be neglected, calculate the amplitude of the response, X0, when m = 150 kg, k = 5 MN/m, F0 = 450 kN and rad/s.

A motor of weight m is supported by a mounting that has spring constant k. If the unbalance of the motor is equivalent to a force and damping can be neglected, calculate the amplitude of the response, X0, when m = 150 kg, k = 5 MN/m, F0 = 450 kN and rad/s.

Is the following statement true or false? In the products of methylation-hydrolysis, every -OH group corresponds to the position of a glycosidic bond in the starting polysaccharide.

Which of the follwoing structures represents amylopectin?

Which of the following is true about an aldopentose?I. It is a monosaccharide.II. It contains a CHO groupIII. It is a disaccharide.IV. It is an oligosaccharide.

For stock A, we have 𝛽 𝑖 = 0.70. Suppose the expected market risk premium next year is 9% and the risk-free rate is 3%. What is the expected return of this stock based on the CAPM? (Please answer in % and round to 2 decimal places. If the answer is 8.057%, then in the box, write 8.06)

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单