Recent content by Dustinsfl

Homework Statement Prove that if ##n^2## is divided by 3, then also n can also be divided by 3. Homework EquationsThe Attempt at a Solution Is there anything wrong with this argument? By contradiction, suppose ##3|n## and 3 doesn't divide ##n^2##. Then ##3m = n##. Multiple both sides by...

b = 1in or 0.0254 m 0.23 is by definition of equivalent mass of a cantilever beam. I don't know. I am trying to determine the force transmitter to the base.

A steel cantilever beam is ##120## in long by ##1\times 1## in##^2## which has a motor that weighs ##100## lb##_f## mounted at the end. The motor runs at 183.26 rad/sec. The motor has an unbalance of ##0.1## lb##_m## located at a radius of ##0.1## in from the axis of the shaft. Assume that for...

It is a cantilever beam with end load.

What do you mean?

I am not sure on how I would design a tuned mass damper from the paper though. I am trying to design one for a system with ##M = 55## kg and a tuned mass damper weighing ##5.5## kg. The natural frequency of the system is ##\omega_n = 12.061## and the forcing function has ##\omega = 183.26##.

It has $$ \mu = m/M $$ Is ##M## total mass of the system prior to the damper or is the total mass plus the damper mass of m?

Homework Statement I have been searching online but I am unable to find a site that explicitly states the Den Hartog criteria for a tuned mass damper. What is the Den Hartog criteria? Homework EquationsThe Attempt at a Solution

Homework Statement How does one determine the amplitude of the force transmitted to the base of a beam? Homework EquationsThe Attempt at a Solution The ODE modeling displacement is $$ -0.000891(9.60875\sin(183.26t) - 323.778\sin(5.4386t)) $$

Homework Statement ##M\ddot{y} + k_{eq}y = me\omega^2\sin(\omega t)## What is ##m##? Homework EquationsThe Attempt at a Solution In the ODE above, ##M## is the total mass of the problem, correct? For instance, if we had a cantilever beam, ##M = m_b + m_m(0.23)## where ##m_b## is the mass of...

Thanks. I divided m by k instead of the other way around.

Homework Statement I am trying to find a damping ratio. I know ##k=50## lb##_f##/in, ##m=50## lb, ##c = 0.75## lb##_f##-sec/in. Homework Equations ##1## lb##_f##/in = ##175.1268## N/m ##1## lb = ##0.4536## kg The Attempt at a Solution Then ##k = 8756.34## N/m, ##c = 131.345## N/m-sec, and ##m...

You need to find y(t) for the ROC.

I guess I need to break it down Barney style for you. There are 4 arms so y_i where i is 1,2,3,4 are the arm displacement. I then said the body I am using z. That means the equation which isn't a constraint must be the displacement of the whole quad rotor if we view it as a rigid body. Also the...

You can use the Bromwich integral to find the inverse Laplace transform. The poles of ##s## are ##s = \frac{-a\pm\sqrt{a^2 + 4b}}{2}## \begin{align} \mathcal{L}^{-1}\Bigl\{\frac{1}{s^2 + as - b}\Bigr\} &= \frac{1}{2\pi i}\int_{\gamma -i\infty}^{\gamma +i\infty}\frac{e^{st}}{s^2 + as - b}ds\\ &=...