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

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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
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
S=2 U=0 T=0
5. Consider modeling the vertical suspension system of a small sports car as a single degree of freedom system of the form: mx + cx' + kx = 0 where m is the mass of the car and c and k are the equivalent damping and stiffness of the four-shock-absorber-spring systems. The car deflects the suspension system 0.05 m under its own weight. The suspension is designed to have a damping ratio of 0.3. a) Calculate the suspension system's equivalent damping and stiffness coefficients, if the car has a mass of 1500 kg. Also, determine the natural frequency. b) Then, with the same suspension, if two passengers, a full gas tank, and luggage totaling 350 kg are loaded in the car, determine the natural frequency and damping ratio. c) Comparatively discuss the results provided in parts (a) and (b) in terms of damping capacity, natural frequency, the amplitude of vibration, and time duration for vibration to nearly stop.

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