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.

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  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.

BlackTom AI · Accepted Answer

The problem describes a single-degree-of-freedom system where a mass-spring setup experiences a harmonic unbalance force F0 due to motor operation, with damping neglected. The standard steady-state displacement amplitude under harmonic forcing is given by X0 = F0 / sqrt((k - m ω^2)^2 + (c ω)^2). Since damping c = 0 in this scenario, the expression simplifies to X0 = F0 / |k - m ω^2|.

Now, let's examine the data provided. The mass m = 150 kg and the spring constant k = 5 MN/m = 5×10^6 N/m are clear. The force amplitude is F0 = 450 kN = 450×10^3 N, which is also clear. However, the problem statement is missing the excitation angular frequency ω (it shows “and   rad/s,” with the numeric value omitted). Without ω, we cannot compute the denominator |k − m ω^2|, and therefore we cannot determine a numeric amplitude X0.

Here are the key checks for the given quantities:
- If ω is known, compute m ω^2, subtract from k, take the absolute value, and divide F0 by that result to get X0 in meters. If the result is 0 (i.e., k = m ω^2), the amplitude would be infinite in this idealized, undamped case, signaling a resonance condition with damping neglected.
- The units are consistent: F0 in newtons, k in newtons per meter, m in kilograms, ω in radians per second, so m ω^2 has units of N/m, matching k.

Because the excitation frequency is missing, any numerical evaluation of X0 (including a value like 15.8 cm) would be speculation. If ω were provided, one could proceed as follows: compute Δ = |k − m ω^2|, then X0 = F0 / Δ, and finally convert to centimeters if needed (X0 [m] × 100 to get [cm]).

In summary, the calculation hinges on the missing ω value. Once ω is supplied, substitute into X0 = F0 / |k − m ω^2| to obtain the amplitude, and convert to centimeters if the final answer should be in cm.

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. 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 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.

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.

What was the world's first widely adopted biodiversity policy?

The aim of the Paris Agreement is to ensure that the earth’s preindustrial temperature is not exceeded by more than º Celsius.

The IPCC's mission is to Blank ______.

Why have most international agreements for environmental protection been based on the honor system?

As was exhibited with the Montreal Protocol and the encouragement of reduced CFC production, trade can be an effective tool to compel compliance with international treaties.

The Stockholm Declaration and UNEP were the result of the Blank ______ first conference on the Human Environment in 1972.

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