### ENMEC4060 Vibration and machine dynamics - Assessment task

**Problem 1**

An unbalanced flywheel shows an amplitude of 0.165 mm and a plan angle of 15° clockwise from the phase mark. When a trial weight of magnitude 50 g is added at an angular position 45° counter-clockwise from the phase mark. the amplitude and the phase angle become 0.225 mm and 35° counterclockwise. respectively. Find the magnitude and angular position of the balancing weight required. Assume that the weights are aided at the same radius.

**Problem 2**

Masses of 1 kg, 3 kg, and 2 kg are located at radii 50 mm, 75 mm, and 25 mm in the plane C, D, and E, respectively, on a shaft supported at bearings B and F. as shown in the accompanied figure. Find the masses and angular locations of the two balancing masses to be placed in plane A and G so that the dynamic load on the bearings will be zero.

**Problem 3**

The arrangement of cranks in a six-cylinder in-line engine is shown in the figure. The cylinder are separated by a distance a in the axial direction and the angular positions of the cranks are given by a_{1} = a_{6} = 0°, a_{2} = a_{s} = 120°, and a_{3} = a_{c} = 240°. If the crank length connecting-rod length. and the reciprocating mass of each cylinder are r, l, and m, respectively. find the primary and secondary unbalanced forces and moments with respect to the reference plan indicated in the below figure.

**Problem 4**

Find the equations of motions, natural frequencies, and modal sectors of only three of these systems

**Problem 5**

Two identical pendulums, each with mass m, and length, l, are connected by a spring Trull; of stiffness k at a distance d from the fixed end. as shown in the bans figure.

a) Dense the equations of motion of the two masses

b) Find the natural frequencies and mode shapes of the system.

c) Fund the free-s :Matron response of the system in the maul conditions θ_{1},(0) = θ_{2}(0) = 0,θ_{1}(0) = 0, and θ_{2}(0) = 0

**Problem 6**

For the four-story shear building shown in the below figure. there is no rotation of the bortiontal section at the lend of doors. Assunung that the floors are rigid and the total mass is concentrated at the levels of the floors. drive the equations of motion of the budding using (a Newton's second law of motion and (b) Lagranges equations.

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