The base of a spring-mass-damper system undergoes a harmonic motion driven by a

Question

The base of a spring-mass-damper system undergoes a harmonic motion driven by a shaker, as shown in Fig. 2. The symbol y(t) denotes the displacement of the base, and x(t) describes the displacement of the mass from its static equilibrium position at time

t. It is known that the mass m = 1,000 kg, spring constant k = 500 kN/m, damping ratio ? = 0.4, and driving frequency of the shaker is ? dr = 40 rad/s. Determine the mass displacement x(t), when the base has a displacement of y(t) = 0.06 m   

Explanation / Answer

we know from the relation

w = (k/m)^1/2

or w^2 = k/m

or m = (k/w^2)

where m is mass,k = 500 kN/m = 500 x 10^3 N/m and w = 40 rad/s

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.