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.

How did Egyptian culture and governance change during the Ptolemaic period compared to the pharaonic period?

Name the Supreme Court decision that removed financial constraints on PACs.

Political scientists Joshua Kalla and David Broockman find that senior policy makers made themselves available to _____ between three and four times more often than they did to constituents.

Name the political scientist who argues that parties are designed to serve the needs of ambitious politicians (namely candidates and officeholders).

Name the political scientist who said this famous quote about the problems of pluralism: “The flaw in the pluralist heaven is that the heavenly choir sings with a strong upper-class accent.”

What is the name of the third party candidate in 2000 who was not allowed to participate in the presidential debates? Hint: We watched a video clip with him in class.

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