1. A foot pedal mechanism can be roughly modeled as a simple pendulum connected to a springmodeled as a pendulum connected to spring as depicted below. The purpose of the spring isto provide a return force for the pedal action. Compute the spring stiffness needed to keepthe pendulum at 1° from the horizontal line and then obtain the natural frequency. Assumethat that the angular deflections are small. Note that the pedal is horizontal when the springis at its free length. The values in the figure are m = 0.5 kg, g = 9.8m/s², l₁ 0.2 m, and12 = 0.3 m.4₁www12k0m8

Detailed step by step solution is given below, still if you have any query please feel free to…

Answered: 1. A foot pedal mechanism can be…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Similar questions

Seen in Figure 1, a rotating mass (with mass moment of inertia Id to a fixed wall (on the far left) by a torsional spring (k 1kg* m² and angular position a) is attached 1Nm/rad) and a torsional damper. Consider the spring and damper as concentric and in parallel. Dampers with damping ratios of c = be considered. Att = 0.1, 0.5, 1.0, and 1.5kg * m²/s will 0, a unit step torque Tin is applied to the rotating mass. A unit step input is a forcing function whose value is 0 from -∞o to some time to and 1 from to to oo. Here, to = 0. Your tasks: k ww + C = la Od A Derive the equation of motion of the rotating mass. Write c as EOM's for the different values of c. Tin 0 Figure 1: Schematic of the mechanical system to model in Problem 1. em, you will solve part B over MA AB Grader Plea LO onment variable. You do not need to write separate ד ו. for
PARTS A & B solve carefully and label each part and CIRCLE FINAL ANSWER ( Use image Below) Part A - Assuming the elements are all linear, determine a model for the mass-spring-damper system. Make sure to clearly define the direction of positive velocity. Simplify your answer such that the model is in terms of the parameters (?, ?, ??, ??), the input force (?), the spring deflection and the mass velocity as well as their time derivatives. Part B - Take the ANSWER from PART A and replace the damping constant ? with the nonlinear expression ? = ?? + ?? + ? , with ? as the velocity of the mass.
2. Consider the following compound pendulum, which consists of a thin rod attached to a pivot point 1/3 down its length, and has a thin disk of radius R attached to the end. Mass of the rod is m, and mass of the disk is me. Tasks: a. Find an Equation of Motion for rotational motion of the pendulum. Assume 0 <15° and apply the small angle approximation. b. Find the natural frequency w of this system. Report in terms of mr, ma, I, R, and g.
The quarter-car model of a vehicle suspension and its free body diagram are shown in Figure 1. In this simpliﬁed model, the masses of the wheel, tire, and axle are neglected, and the mass m represents one-fourth of the vehicle mass. The spring constant k models the elasticity of both the tire and the suspension spring. The damping constant c models the shock absorber. The equilibrium position of m when y=0 is x=0. The road surface displacement y(t) can be derived from the road surface profile and the car’s speed. Draw free body diagram (FBD) and derive the equation of motion of m with y(t) as the input, and obtain the transfer function. If assume: m=300 kg k=20000, 40000, 60000 N/m c=1000, 3000, 5000 N.s/m Plot magnification ratio vs frequency ratio (r=0-4) diagrams for the parameters given above (you can draw the three curves in one diagram for three different k values and do the same for the three c values as well). Use the derived transfer function to model the system and plot…
8. A control pedal of an aircraft can be modeled as the single - degree of freedom system of figure below. Consider the lever as a massledd shaft and the pedal as a lumped mass at the end of the shaft. Use the energy method to determine the equation of motion in and obtain the natural frequency of the system. Assume the spring to be unstretched at 0 = 0 and gravity points down. www 1/₂
3. A vibrating mass-spring system exhibits an acceleration amplitude of 27 mm/s² and a dis- placement amplitude of 2 mm. Compute the system's natural frequency.
+ b 3. A tuning fork is an example of a "resonant system", that is, one that has a low damping ratio. A model of a (half) tuning fork is rod of mass m with air drag modeled as a damper connected approximately at its middle, and a torsional spring at the base of the cantilever. Assume the cantilever rotates back and forth about its pivot by a small angle o. Because other forces are much larger, you can reasonably neglect the effect of gravity in this model. The moment of inertia of a cantilevered beam pinned at one end is equal to ml2, where I is its length. (a) What is the natural frequency of this system if m= 0.1 kg and k = 2548 Nm/rad, and 1 = 0.1 m. Please give the value in rad/s and Hz. (b) Find an upper bound on the damping coefficient b that insures that the damping ratio of the tuning fork is no greater than = 0.01. (c) For this damping ratio, what is the damped natural frequency of the system? (d) For this damping ratio, what is the decay rate (the size of the exponent…
A factory machine with a mass of 320 kg vibrations up and down with frequency of 8 Hz. Amplitude of engine movement of 2 mm. Calculate the maximum acceleration of the machine, and what is the maximum Newtonian force obtained?
Present the equations of motion of the attached two-degree-of-freedom system in the main coordinate system. Determine a value for α such that the equations of motion can be solved in the principal coordinate system. If it is assumed that the type of damping is Rayleigh damping (10% proportional to mass and the rest proportional to stiffness), then determine the relative damping coefficient and damping constants for the structure.
A body weighing 5kg is attached to a very light bar as depicted below. The set-up is free to rotate in the vertical plane about pin support O. The force applied at point C makes the bar oscillate(via small rotation) about the position of equilibrium illustrated below a. Derive the differential equation of motion for the steady state angular displacement (theta) of the bar

Recommended textbooks for you

Elements Of Electromagnetics

Mechanical Engineering

ISBN:

9780190698614

Author:

Sadiku, Matthew N. O.

Publisher:

Oxford University Press

Mechanics of Materials (10th Edition)

Mechanical Engineering

ISBN:

9780134319650

Author:

Russell C. Hibbeler

Publisher:

PEARSON

Thermodynamics: An Engineering Approach

Mechanical Engineering

ISBN:

9781259822674

Author:

Yunus A. Cengel Dr., Michael A. Boles

Publisher:

McGraw-Hill Education

Elements Of Electromagnetics

Mechanical Engineering

ISBN:

9780190698614

Author:

Sadiku, Matthew N. O.

Publisher:

Oxford University Press

Mechanics of Materials (10th Edition)

Mechanical Engineering

ISBN:

9780134319650

Author:

Russell C. Hibbeler

Publisher:

PEARSON

Thermodynamics: An Engineering Approach

Mechanical Engineering

ISBN:

9781259822674

Author:

Yunus A. Cengel Dr., Michael A. Boles

Publisher:

McGraw-Hill Education

Control Systems Engineering

Mechanical Engineering

ISBN:

9781118170519

Author:

Norman S. Nise

Publisher:

WILEY

Mechanics of Materials (MindTap Course List)

Mechanical Engineering

ISBN:

9781337093347

Author:

Barry J. Goodno, James M. Gere

Publisher:

Cengage Learning

Engineering Mechanics: Statics

Mechanical Engineering

ISBN:

9781118807330

Author:

James L. Meriam, L. G. Kraige, J. N. Bolton

Publisher:

WILEY

SEE MORE TEXTBOOKS