Page 51 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

38 Free Vibration Chap. 2

PR O BL EM S

2-1 A 0.453-kg mass attached to a light spring elongates it 7.87 mm. Determine the natural
frequency of the system.
2-2 A spring-mass system, A:j and m, has a natural frequency of /i- If a second spring A:2
is added in series with the first spring, the natural frequency is lowered to
Determine k2 \n terms of /cj.
2-3 A 4.53-kg mass attached to the lower end of a spring whose upper end is fixed vibrates
with a natural period of 0.45 s. Determine the natural period when a 2.26-kg mass is
attached to the midpoint of the same spring with the upper and lower ends fixed.
2-4 An unknown mass of m kg attached to the end of an unknown spring k has a natural
frequency of 94 cpm. When a 0.453-kg mass is added to m, the natural frequency is
lowered to 76.7 cpm. Determine the unknown mass m and the spring constant k
N/m.
2-5 A mass hangs from a spring k N/m and is in static equilibrium. A second mass m2
drops through a height h and sticks to without rebound, as shown in Fig. P2-5.
Determine the subsequent motion.

'"I Figure P2-5.

2-6 The ratio k/m of a spring-mass system is given as 4.0. If the mass is deflected 2 cm
down, measured from its equilibrium position, and given an upward velocity of 8 cm/s,
determine its amplitude and maximum acceleration.
2-7 A flywheel weighing 70 lb was allowed to swing as a pendulum about a knife-edge at
the inner side of the rim, as shown in Fig. P2-7. If the measured period of oscillation
was 1.22 s, determine the moment of inertia of the flywheel about its geometric axis.

Figure P2-7.