Mechanical Vibrations Questions

(See attached file for full problem description with diagrams) Mechanical Vibrations Question No.1 A pulley 250mm in diameter drives a second pulley 1000mm diameter by means of a belt.The mass moment of inertia of the drive pulley is 0.2kg-m2. The belt connecting these pulleys is represented by two springs, each of stiffness k. Find a value for k for which the natural frequency is 6 Hz. Derive the equation of motion for this system. Mechanical Vibrations Question No. 2 A DVD drive is mounted on a chasis and is modelled as a single degree of freedom spring, mass and dampener. During normal operation, the drive (having a mass of 0.4kg) is subject to harmonic force of 1N at 10 Radia... click for more

Matrix equation of motion

1) For the two degree of freedom structure shown: i) what is the matrix equation of motion?. Assume that m1 and m2 oscillate harmonically with the same frequency but with different amplitudes X1 and X2 of x1(t) and x2(t). ii) what are the values of the amplitude ratios r1 and r2 if m1 = m2 = m, k1 = k, and k2 =3k? See attached file for full problem description.

Please show me formula, explain and what is the correct answer.

1) In the idealized model attached shown, m = 15 kg, k = 135 N/m, and the viscous damping ratio is 0.15. Assume that an external harmonic force F(t) = 15 cos 4 t acts on the system with F0=15 N and forcing frequency of 4 rad/s. i) Find the magnification factor M for the frequency ratio r of 1.382. ii) What is the amplitude of the response X? For i ), which one is correct answer: (a) 4 (b) 3 (c) 1 For ii ), which one is correct answer: (a) 0.127 (b) 0.184 (c) 0.274

A machine tool having a mass of 1000 kg and a moment of inertia J = 300 kg-m2, is supported on elastic supports with stiffnesses and locations shown.

1) A machine tool having a mass of 1000 kg and a moment of inertia J = 300 kg-m2, is supported on elastic supports with stiffnesses and locations shown. i) Find the natural frequencies of the machine tool. ii) what are the corresponding amplitude ratios? (There are 2 separate questions in 1 problem). Please see attached figure. For i ), which one is correct answer: (a) 35.63 rad/s, 41.17 rad/s (b) 58.70 rad/s, 62.37 rad/s (c) 41.17rad/s, 57.82 rad/s (d) 70.58 rad/s, 82.37 rad/s See attached file for full problem description. For ii ), which one is correct answer: (a) -2.383, 0.185 (b) -5.348, 0.056 (c) -7.242, 0.024

Two degree of Freedom Systems

A Problem about Two degree of Freedom Systems. See attached file for full problem description.