So and
Thus, we have so that meaning
is the particular solution
The general solution is
Initial conditions imply so
Thus,
Where transient solution is and steady state solution is
For the given values of m, c, k, and f(t), assume the forced vibration is initially at equilibrium. For t 0, find the m...
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)
Consider a damped forced mass-spring system with m = 1, γ = 2, and k = 26, under the influence of an external force F(t) = 82 cos(4t). a) (8 points) Find the position u(t) of the mass at any time t, if u(0) = 6 and u 0 (0) = 0. b) (4 points) Find the transient solution uc(t) and the steady state solution U(t). How would you characterize these two solutions in terms of their behavior in time?...
Question 4 The equation of motion of a forced vibration problem is given by d-x dx, m- *+kx = Pcos(wt) dt? dt Given the values, m = 6.45, r = 67.42, k = 398.01, P = 5.6 and W = 6.42. Determine the steady-state solution, xp(15.12) of the differential equation, giving your answer correct to 3 decimal places.
Consider the forced vibration in Figure 1. We mass, m Figure 1: Forced Vibration 1. Use a free-body diagram and apply Newton's 2nd Law to show that the upward displacement of the mass, r(t), can be modelled with the ODE da da mdt2 + cat + kz = F(t) where k is the spring coefficient and c is the damping coefficient. = 2 kg, c = For the remainder of the questions, use the following values: m 8 Ns/m, k...
damped forced mass-spring system with m 2, and k 26, under the 2 Consider a influence of an external force F(t)= 82 cos (4t) 1, 7 = a) (8 points) Find the position u(t) of the mass at any time t, if u(0) 6 and u'(0) = 0. b) (4 points) Find the transient solution u(t) and the steady state solution U(t). How would you characterize these two solutions in terms of their behavior in time? We were unable to...
ONLY attempt to solve if you know what you are doing. A mass of 1 kg is attached to a spring whose constant is 5 N/m. Initially, the mass is released 1 m below the equilibrium position with a downward velocity of 5 m/s, and the subsequent motion takes place in a medium that offers a damping force that is numerically equal to 2 times the instantaneous velocit y. a) Find the equation of motion if the mass is driven...
04: Let m = 2g, c = 0.08g/sec, and k = 20g/sec?, in a forced oscillation system under a non-sinusoidal periodic driving force, and f(t) = { t, -t, --1/2 <t</2 TI/2 < t <31/2 f(t) = f(t + 210) (15Marks) Find the steady-state solution?
Question 1 Suppose m-2 kg, k- 32 N/m and F() is an odd periodic force with a period of 2 s given in one period by ON if O<t<I Construct the steady periodic motion, Xsn) using the Fourier series. Question 1 Suppose m-2 kg, k- 32 N/m and F() is an odd periodic force with a period of 2 s given in one period by ON if O
QUESTION 2: Consider this forced translational mass-spring-damper (MSD) system: The input is the external force "F(t)" and the output is position "x(t)." The transfer function for this system is g) - 6 - Mz? +BS+K It is known that M - 1 kg. B - 10 mm, and there are three possible values of K: (K = 16 K = 34 NK-89 The only possible external forces "F(t)" have the following Laplace transforms: 1) F,(s) - 0 (corresponding to external...
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...