Q3:(10 MARKS)A piston with a weight of 29.4 N is supported by a springand dashpot. A dashpot of damping coefficient c = 275N.s/m acts in parallel with the spring of stiffness k = 2400N/m. A fluctuating pressure p = 960 sin 30t N/m² acts onthe piston, whose top surface area is 0.05 m². Determinethe steady-state displacement as a function of time and themaximum force transmitted to the base.P=Po sin cotW

Answered: Q3: (10 MARKS) A piston with a weight…

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

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A single degree of freedom mass-spring-viscous damper system with mass m, spring constantk and viscous damping coefficient q is critically damped. The correct relation among m, k, and q is q = 2km q = 2/ km 2k = b m k q =2
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Whats the first equation (circled) and how did we get it ?
1- Two mass-spring-damper systems A & B. System A has = 0.1 and @n = 20 rad/sec, and system B has < = 0.3 and wn = 5 rad/sec. Which system will vibrate longer in time? Why?
The motion of a damped spring-mass system is described by the following ordinary differential equation m * d2x/dt2 + c * dx/dt + k*x = 0 where x = displacement from equilibrium position (in meters), t = time (seconds), m = 20-kg mass, and c = the damping coefficient (N . s/m). Take the damping coefficient c = 5 and the spring constant k = 20 N/m. The initial velocity (dx/dt) is zero, and the initial (t=0) displacement is x = 1 m. Solve analytically.
An undamped simple harmonic oscillator has mass 2.0 kg and spring constant 50 N/m. The initial displacement from equilibrium (at time t = 0) is 0.30 m and the initial velocity is 2.0 m/s. %3D 1. Determine the angular frequency (in rad/s), the frequency (in Hz), and the period (in s). Determine numerical values (not in terms of .) Determine the displacement in the form x(t) = Acos(mot) + Bsin(@ot). That is, solve for A and B in meters, and write oo in radians per second.
Fig. (2) Q3-A (8 Marks): An automobile is modeled as a single-degree-of-freedom system vibrating in the vertical direction. It is driven along a road whose elevation varies sinusoidally. The distance from peak to trough is 0.2 m and the distance along the road between the peaks is 35 m. If the natural frequency of the automobile is 2 Hz and the damping ratio of the shock absorbers is 0.15, determine the amplitude of vibration of the automobile at a speed of 60 km/hour 6.18
Suppose a spring with spring constant 7 N/m is horizontal and has one end attached to a wall and the other end attached to a 2 kg mass. Suppose that the friction of the mass with the floor (i.e., the damping constant) is 1 N⋅s/m a) Set up a differential equation that describes this system. Let x to denote the displacement, in meters, of the mass from its equilibrium position, and give your answer in terms of x,x′,x′′. Assume that positive displacement means the mass is farther from the wall than when the system is at equilibrium. b) Find the general solution to your differential equation from the previous part. Use c1 and c2 to denote arbitrary constants. Use t for independent variable to represent the time elapsed in seconds. Your answer should be an equation of the form x=… c) Enter a value for the damping constant that would make the system critically damped. ?Ns/m
Please help. This problem involves a mass spring damper system. Thank you.
Q2 The angular position c of a mass is controlled by a servo system through a referen signal °r. The moment of inertia of moving parts referred to the load shaft, J, is 150 kebo and damping torque coefficient referred to the load shafi(B, is 4.5 x 103 Nw-m fraden The torque developed by the motor at the load s 7.2 x 10* Nw-m per radian of error (a)Obtain the response of the system to a step input of 1 rad and determine the peak time, peak overshoot and frequency of transient oscillations. Also find the steady state error for à constant angular velocity of 1 revolution / minute. (b)If a steady torque of 1000 Nwm is applied at the load shaft, determine the steady Kan state error. 5(J5+ B) 03 For the system shown, apply a proportional controller to move the time constant to a sixth of its open loop value. R(s) + E(s) U(s) Kp 'Y(s) s +0.333 10
Consider the spring mass damper system shown below. k m x(t) The forces of the spring and damper are represented by Fspring = -kx and Fdamper = -bx' respectively, where k is the spring constant and b is the damping coefficient. The mass has an initial displacement +1 m and velocity 0 m/s. 1. Use Newton's 2nd Law of Motion to derive an ODE to describe the mass's motion. 2. Find x (t) for m = 2 kg, b = 1 N s/m and k = {0.1,0.3,0.5} N. m. What happens when the stiffness of the spring is being increased?
Q2) a vibratory system with viscous damping: Mass = 2.5 kg; spring constant k = 3 N/mm and the amplitude X decreases to 0.25 of the initial value after five consecutive cycles. Determine the damping coefficient of the damper in the system. k spring G b damper m mass x(t) Time

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