Question 4 The equation of motion of a forced vibration problem is given by d-x dx,...
2. The equation of motion for an undamped forced vibration system is given as, * + 169x = 40t Determine the response by Convolution Integral method
For the given values of m, c, k, and f(t), assume the forced vibration is initially at equilibrium. For t 0, find the motion x(t), and identify the steady-periodic xs(t) and transient Xtrt) parts m 1, c4, k 5, f(t) 20 cos(3t) x(t) ain(3)cos (3t) xsp(t)= xtr(t) For the given values of m, c, k, and f(t), assume the forced vibration is initially at equilibrium. For t 0, find the motion x(t), and identify the steady-periodic xs(t) and transient Xtrt)...
QUESTION 2 (20 MARKS) a Consider the vibration of mass spring system given by the initial value problem dx dx de+b + kx = 0 dt *(0) = 0 . x'(0) = 1 Where m, b, k are nonnegative constants and b2 < 4mk. Show that a solution to the problem is given by X(t) = 2m Amk- em sin 4mk-02 2m (CO2:P01 - 8 Marks) b. A 200 g mass stretches a spring 5 cm. If it is release...
For the given values of m, c, k and f(t), assume the forced vibration in a spring-mass dashpot system is initially at equilibrum. For t>0, find the motion x(t) and identify the steady periodic and transient parts m=2, c=2, k=1, f(t)= 5cos(t)
help me with this Consider the vibration of mass spring system given by the initial value problem m d²x dt2 dx +b. dt + kx = 0 x(0)=0, x'(0) = 1 Where m, b, k are nonnegative constants and b2 < 4mk. Show that a solution to the problem is given by b2 2m e 2m sin 4mk-b2 4mk 2m t (CO2:P01 - 8 Marks) b. A 200 g mass stretches a spring 5 cm. If it is release from...
Answer all parts of the question please! Consider the equation one gains from considering forced oscillations applied to a damped system d2y Fo -y= m c dy k cos(wt) dt2 m dt (a) Show that yp is a particular solution where, Fo - mw2) cos(wt) c sin(wt)). Yp(t) mw2)2 c2w2 - This can be written as Fo cos(wt - n), Ур (t) — where H and n are constants, independent of time. (b) Using this particular solution and the solution...
6. A second order differential equation d?x/dt+ 5 dx/dt+7x = 7y. State the undamped natural frequ damping ratio. 7. State the damped natural frequency, damping coefficient and time constant for question 6. 8. Given that the transfer function G is K/s(s+sT). State the type and order of the system 9. It is given that G(s) = K/s (1+sT). This system is operated in a closed-loop with unity feedback. W order and the type of closed-loop system? 10. Given the transfer...
Problem 1.Consider the harmonically forced undamped oscillator described by the following ODE:mx′′+kx=F0cosωt, k >0, m >0, ω >0, F0∈R. Problem 1. Consider the harmonically forced undamped oscillator described by the following ODE: mx" + kx = Fo cos wt, k > 0, m > 0,w > 0, F0 E R. (1) a) Suppose wa #k/m. Find the general solution of the ODE ). b) Consider the initial value problem of the ODE () with initial conditions x(0) = 0 and...
Q.3 (Applications of Linear Second Order ODE): Consider the 'equation of motion given by ODE d²x 102 +w²x = Focos(yt) where Fo and wty are constants. Without worrying about those constants, answer the questions (a)-(b). (a) Show that the general solution of the given ODE is [2 pts] Fo x(t) == xc + Ip = ci cos(wt) + C2 sin(wt) +- W2 - 92 cos(7t). (b) Find the values of ci and c2 if the initial conditions are x(0) =...
Q in n D.O.F system’s equations of motion, Write sequence of forced vibration analysis M=mass matrix K=stifeness matrix C=proportional damping matrix f(t)= external vector x= state vector 문제4) 임의의 입력을 가지는 n D.0.F system의 운동방정식은 다음과 같이 기술 된다. madal analysis에 의한 강제진동 해 석 순서를 기술하여라. 이 때 M은 지량행 렬, K는 강성 행렬, C는 비례 댐핑행렬, 는 상태 벡터, f(t)는 외력 벡터이다. Mx+ Ca+ Kx = f(t) 여기서 비례댐핑(proportional C는 damping)의 경우에 제한한다. 문제4) 임의의 입력을 가지는 n...