Please code in Python P1) The motion of a damped spring-mass system is described by the following ordinary differentialequation:md²x dx+c +kx=0dt²dtm = 20 kgwhere x = displacement from equilibrium position (m), t = time (s), c = damping coefficient (N⚫s/m). Thedamping coefficient, c, takes on three values of 5 (underdamped), 40 (critically damped), and 200(overdamped). The spring constant is 20 N/m. The initial velocity is zero, and the initial displacement isx = 1 m. Solve this equation using the numerical method we have learned in class over the period of timefrom 0 to 15 s. Plot the displacement versus time for the three cases of the damping coefficient on thesame plot.m

First, let's go through the given equation that describes the motion of a damped spring-mass system:…

Answered: P1) The motion of a damped spring-mass…

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

Please answer question number 1.
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
Whats the first equation (circled) and how did we get it ?
4 QUESTION 20 The car bridge in Figure Q20 can be modelled as a damped-spring oscillator system with mass M = 10000 kg, spring coefficient k = 50000 N-m-1 and damping constant c = 50000 N-s-m-1. Cars cross the bridge in a periodic manner such that the bridge experiences a vertical force F (N) expressed by F = mg sin(10t) where m = 1136 kg is the average mass of passing cars, g = 9.81 m-s-2 is the gravitational acceleration and t (s) is the time. Determine the maximum force magnitude transmitted to the foundation (see Figure Q20) during the steady-state oscillatory response of the system. Provide only the numerical value (in Newtons) to zero decimal places and do not include the units in the answer box. E m M foundation Figure Q20: Vibrating car bridge.
The 8kg body is moved to the right of the equilibrium position and released from rest at time t = 0. The viscous damping coefficient is 23NS/m and the spring stiffness, K is 38N/m. Determine the damping factor (ratio) of the system. Note: Give your answer to 3 decimal places. Other Parameters: Logarithmic Decrement (8): Answer: 2ng 2T C 8 = In = In1 = 5 wnTd = 5wn X2 Xn+1 1-5 wa 2m k Damping Ratio (5): 5= 2vkm 2mn V(21)2+8 Frequency of damped vibration (wa): wa = 1-Wn Undamped Forced Vibration: Frequency Ratio (): r- Xp-x sin w t Next page Hous page Type here to search
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.
umang
A mass-spring system is driven by the external force g(t) = 2 sin3t + 10 cos 3t. The mass equals 1, the spring constant equals 5, and the damping coefficient equals 2. If the mass is initially located at y (0) =-1, with initial velocity y' (0) = 5, find its equation of motion to find y (1). Round up the answer to the second decimal place point.
Please help. This problem involves a mass spring damper system. Thank you.
Mecjanical Vibration
2- A damped single degree of freedom mass-spring system has a mass m = 5 kg, a spring stiffness k = 3,125 N/m, and a damping coefficient c = 25 N. s/m. The mass is subjected to a harmonic force which has an amplitude F₁ = 20 N and frequency w₁ = 10 rad/s. The initial conditions are such that x0 = 2 cm and v₁ = x = 0 m/s. Determine the displacement, velocity, and acceleration of the mass after t = 1 s. Determine the magnification factor and phase angle.
1. a) The equation of motion of a weight, m, attached to a spring and a dashpot damping device is 2 y(t) = e| -2cos 3t –sin 3t 3 where y(t), measured in feet, is the displacement from the equilibrium position of the spring system and is measured in seconds, see Figure 1. Find the initial position and the initial velocity of the weight, m. Give physical interpretations on your answers. y = 0 (equilibrium position) m Figure 1

SEE MORE QUESTIONS

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