MIME 3370 Exam 2 Fall 2007
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- (35 points) The upper end of spring k is forced to oscillate with displacement,, where y0= 0.01 m and = 5 rad/sec.
a)(10 points) Derive the equation of motion.
b)(25 points) Find the displacement of the mass, x(t)if both the initial displacement and velocity are zero. k= 100 N/m, m=1 kg.
2) (35 points) a) (20 points) A sinusoidal force , P=0.01 m is applied to a single degree of freedom system with the following properties: . Calculate the steady state response amplitude and phase angle when the frequency of excitation is = 0.01, 4 and 100 rad/sec.
b) (15 points) Solve the same problem if the damping ratio is
3) (30 points) Do not justify your answers to true-false questions (marked T-F). However, you can explain your answer if you think that a question is ambiguous. Answers to the remaining questions must be short (about 50 words). Write your answers on the problem statement.
a)The response of both linear and nonlinear systems to an arbitrary excitation can be calculated using the convolution integral. (T-F)
b)The impulse response of an underdamped system converges to zero faster as the damping ratio increases. (T-F)
c)A unit step force is applied to a system with damping at t=0. The response converges to 1/k as time goes to infinity. (T-F)
d)A unit step force is applied to a system with damping at t=0. The velocity at t=0 is 0. (T-F)
e)Transmissibility of a system is equal to 0 for frequencies very close to zero. (T-F)
f)Transmissiblity is very low when the frequency ratio (frequency of excitation/natural frequency) is very large (say 100). (T-F)