A mass \"m\" of 1kg in the mechanical system is shown below. At t=0 we hit the m

Question

A mass "m" of 1kg in the mechanical system is shown below. At t=0 we hit the mass with an impulsive force p(t) whose strength is 1N. Assuming that the spring constant k=200N/m, b = 20N and the initial conditions are zero.
Find:
a)the displacement x(t) as a function of time t. The displacement x(t) is measured from equilibrium position in the absence of the excitation force.
b) What is the damping condition of the system (over,under,critically)?
c) If k = 200N/m, choose a different b to make the system critically damped. P(t)

Explanation / Answer

a. mx'' + bx' + kx = f(t)

b. m=1kg k= 200 b = 20

jita = b / 2(km)^1/2 = 20/2*200^1/2 = 0.707 <1 underdamped

c. to make it critically damped : jita =1 b =1*2*(200)^1/2 =28.284 N

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