Page 489 - Dynamics of Mechanical Systems

0593_C13_fm Page 470 Monday, May 6, 2002 3:21 PM

470 Dynamics of Mechanical Systems

Section 13.3 The Undamped Linear Oscillator
P13.3.1: For the mass–spring system shown in Figure P13.3.1 let the mass have a weight
of 25 lb and the spring have a modulus of 3 lb/in. Determine the natural frequency and
period of the system.

k = 3 lb/in.

smooth
25 lb

FIGURE P13.3.1
An undamped mass–spring system. x
P13.3.2: See Problem P13.3.1. Suppose that at time t = 0 the mass is displaced 2 in. to the
right and also given a speed of 5 in./sec to the right. Find and express x(t) for the
subsequent displacement of the mass. What is the amplitude of the oscillation?
P13.3.3: Repeat Problem P13.3.1 if the mass is 10 kg and the spring modulus is 6 N/cm.
P13.3.4: See Problems P13.3.2 and P13.3.3. Repeat Problem P13.3.2 if the mass is 10 kg, the
spring modulus is 6 N/cm, the initial displacement is 5 cm to the right, and the initial
speed is 12 cm/sec to the right.
P13.3.5: Consider a simple pendulum with small oscillation. If the pendulum length is
1 m, what is the period? What should be the length if the period is to be 1 second?
P13.3.6: Repeat Problem P13.3.5 if the simple pendulum is replaced by a rod pendulum.

Section 13.4 Forced Vibration of an Undamped Oscillator

P13.4.1: Consider the mass–spring system shown in Figure P13.4.1. Let the block B weigh
15 lb and let the spring modulus be 4 lb/in. Let B be subject to a force F(t) as shown and
given by:

Ft () = 12sin t 8 lb

where t is in seconds. If the system is initially at rest in its equilibrium position, determine
the subsequent motion x(t) of B.

B
k
m F(t)
frictionless
FIGURE P13.4.1
An undamped forced mass–spring x
system.
P13.4.2: Repeat Problem P13.4.1 if initially (t = 0) B is displaced to the right 3 in. and is
moving to the right with a speed of 6 in./sec.
P13.4.3: Repeat Problem P13.4.1 if the block B has a mass of 10 kg, the spring modulus is
8 N/cm, and the forcing function is:

Ft () = 50 sin t 9 N