1. For the systems shown in Figures 1 to 3, a mass m falls ... - ITLiMS

1. For the systems shown in Figures 1 to 3, a mass m falls on a mass m1 and the collision is plastic,
i.e. the two masses move together. Determine the system response.
a
m
B
l
m 1
k
h
m
m 1
k
B
Fig. 1 Fig.2 Fig. 3
2. Having the following items available: weight 1 kg, elastic cord, inextensible cord, stop watch,
measuring tape, slide caliper, plan an entire experiment ( measurements, calculations) to determine
the acceleration of the Earth.
3. A solid homogeneous cylinder of radius r and
height h is pertially immersed in a bath of distilled
water as shown in Fig. Assuming that it remains in
an upright position, plan an entire experiment to
determine the density of the cylinder material ρ c.
4. A fluid damper shown in Fig. has a
piston with m = 0.3 kg and is supported
by a five – turn helical spring of d = 2
mm, D = 20 mm, and G = 1,05 x 10 11
N/m 2 .
a) Find the piston vibration natural
frequency if there is no fluid in the
cylinder.
b) Determine the required damping constant of the damper for critical damping
c) Assuming that the damper fluid is oil, design the piston holes to achive critical damping of
the piston damper. Suppose that light oil with viscosity η = 4 x 10 -3 Ns/m 2 fulfils a chamber.
5. A part of measurement system has a heavy steel dial with m =
0,25 kg. It is placed between two springs as in Fig. The period of
natural vibration of dial – spring system is T = 0,4 s. Redesign the
system to achive:
a) a new period of natural oscillation Tm= 0,25 s
b) time to half T1/2 = 2 s.
D 0
L
h
L
r
a
B
m
l
m 1
D
k

6. A measurement system has a steel dial of length l = 50
mm, width b = 3 mm, and thickness τ = 1mm. The
restoring spring has a rotational spring constant K = 10
Nmm/rad. At a radius r =10mm, there is a dashpot. Design
the dashpot for the following requirement: a time to halt is
equal four periods of natural oscillations, ie.T1/2 = 4T, T =
2π/ω0
7. A periodic vertical force P(t) = P0sinωt as shown in Fig. is
applied to the spring – dashpot - mass system. Equivalent
spring constant is k, mass of a body m, and equivalent damping
coefficient c = 0,2 ckr. Determine the amplitude of the force
acting on the base.
r
K
m
P osinωt
x