FINALS
PROBLEM 1 (10 points)
A 60 gram bullet is travelling at a constant speed of 300 m/s. It hits the 3 kg block, which
is initially at rest, and embeds inside the block, then the block compress the spring and moves
the dashpot. The spring has a constant of 9 kN/m and the dashpot has a coefficient of 400
N-s/m. Determine the displacement, in m, travelled by the block in order to stop the bullet. The
block will only move horizontally all the time.
PROBLEM 2 (10 points)
If the ground is subjected to a shake of 30 Hz and maximum displacement of 15 mm,
find the height of the floor, in meters, of the sample building shown so that the second floor will
have an amplitude of less than 20 mm sidesway. Let the mass of the floor is 1000 kg with a
pillar support on each of its four corners. Each support has circular cross-section area with
diameter of 1 m, and modulus of elasticity of 14 GPa. Neglect the mass of each pillar and the
height of each pillar must be greater than 2 m in order to accommodate people inside.
PROBLEM 3 (8 points)
The T-bar is made from two uniform bar with length 2a and mass m, and welded on the
connection as shown. The one end of the horizontal part of the T-bar has damper with
coefficient c and the other end has spring with constant k. Assuming after given a small
oscillation, determine a) the working differential equation in terms of m, k, c, g, a, and θ, and b)
the critical damping coefficient in terms of m, k, g, and a.
PROBLEM 4 (4 points)
The period of a damped free vibration for a spring-mass model is 0.3 s. If the stiffness of
the spring is 800 N/m and the mass is 1 kg, determine the value of the damping coefficient, in
N-s/m and its logarithmic decrement.
MIDTERMS
PROBLEM 1 (7 points)
Two springs connected to a 15 kg block. When the spring’s configuration is in series
connection, the period is observed to be 1.5 s, it becomes 0.5 s when changed to a parallel
connection. Determine the value of the stiffnesses of the two springs in N/m.
PROBLEM 2 (10 points)
The 8 kg uniform bar AB is hinged at C and is attached to a spring of constant k = 500
N/m. If the end A is given a small displacement so that it will move 5 mm to the left from the
position shown and released, determine the (a) circular frequency, and (b) velocity of B after 1 s.
PROBLEM 3 (7 points)
A cylinder of mass, m and radius, r is suspended from a looped cord as shown. One end
of the cord is attached directly to a rigid support, while the other end is attached to a spring of
constant, k. Determine the natural circular frequency and period of the vibration of the cylinder.
PROBLEM 4 (4 points)
A particle is oscillating in simple harmonic motion plotted in a Cartesian plane where the
abscissa is time (t) in seconds and the ordinate is in displacement (x) in meters. It follows the
equation 𝑥 = 𝐶1 𝑠𝑖𝑛 ω𝑛𝑡 + 𝐶2 𝑐𝑜𝑠 ω𝑛𝑡. The line is measured for its properties and determined
that its amplitude is 2 m and its phase angle is +6.9º. Also, it is measured that when t = 2s, x =
+1.2 m. Determine: a) the complete equation of motion of the particle, b) the maximum velocity
and acceleration of the particle.