Q1) Use Energy method to derive the equation of motion of the simple spring–mass pendulum
system of Figure below and compute the system’s natural frequency. Assume that the pendulum
swings through only small angles so that the spring has negligible deflection in the vertical
direction and assume that the mass of the pendulum rod is negligible.
Q2) A system modeled by the Figure below (Base excitation) , has a mass of 225 kg with a
spring stiffness of 3.5 ×10 4 N/m. Calculate the damping coefficient given that the system has a
maximum deflection of x(t) of 0.7 cm when driven at its natural frequency while the base
amplitude (Y) is measured to be 0.3 cm.
Q3) Consider the base excitation problem for the configuration shown in Figure below. In this case,
the base motion is a displacement transmitted to the mass through a spring element as
demonstrated in the model. The support in the top is fixed, separated from the mass using springdamper. Derive the equation of motion for this system.
Q4) Consider a spring-mass system ( No damping, C=0), exited harmonically by the force,
F(t)= Fo.cos wt. If the system is running at resonance as shown in the displacement plot,
and the particular solution (steady state solution) is suggested as:
xp(t)= t .X sin(wt) as shown in the Figure to the right. Derive a formula to calculate the
magnitude of X.