Dynamics of structures chopra solutions manual free download

A second mass m 2 drops through a height h and sticks to m1 without rebound Fig. Determine the subsequent motion u t measured from the static equilibrium position of m1 and k. The container is accidentally dropped from a height of 3 ft above the ground. Assuming that it does not bounce on contact, determine the maximum deformation of the packaging within the box and the maximum acceleration of the instrument.

The diver oscillates at a frequency of 2 Hz. What is the flexural rigidity EI of the diving board? Substituting Eqs. Substituting this solution into Eq.

Evaluate Eq. Differentiating Eq. The lateral stiffness of the modified system is double that of the original system. Under the lb weight of the car, the suspension system deflects 2 in.

The suspension is designed to be critically damped. In this test, the mass is displaced 1 in. At the end of 20 complete cycles, the time is 3 sec and the amplitude is 0. Determine the stiffness and damping coefficients. Determine damping coefficient. The vertical deflection of the supporting system under the weight of the machine is measured as 0.

The dampers are designed to reduce the amplitude of vertical vibration to one-eighth of the initial amplitude after two complete cycles of free vibration. Find the following properties of the system: a undamped natural frequency, b damping ratio, and c damped natural frequency. Comment on the effect of damping on the natural frequency. How far to the right will the slab move? What is the maximum displacement of the slab on its return swing to the left? If this system is given an initial displacement of 2 in.

In how many cycles will the system come to rest? Substitute for m in Eq. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

Problem 2. Determine the equation describing the motion when the electric current is turned off and the scrap is dropped Fig. Figure P2. Determine the natural frequency. Determine initial deflection. Determine free vibration. Determine the motion of the mass. Set up equation of motion. Solve equation of motion. A bullet weighing 0. Determine the resulting motion u t of the block. A second mass m 2 drops through a height h and sticks to m1 without rebound Fig.

Determine the subsequent motion u t measured from the static equilibrium position of m1 and k. The container is accidentally dropped from a height of 3 ft above the ground. Assuming that it does not bounce on contact, determine the maximum deformation of the packaging within the box and the maximum acceleration of the instrument. Compute the maximum acceleration. Determine deformation and velocity at impact. Compute the maximum deformation.

The diver oscillates at a frequency of 2 Hz. What is the flexural rigidity EI of the diving board? Substituting this solution into Eq. Evaluate Eq. The solution, Eq. Solution: Substituting A and B into Eq. The lateral stiffness of the modified system is double that of the original system. Under the lb weight of the car, the suspension system deflects 2 in. The suspension is designed to be critically damped. The damping ratio is c In this test, the mass is displaced 1 in.

At the end of 20 complete cycles, the time is 3 sec and the amplitude is 0. Determine the stiffness and damping coefficients. Solution: 1. Determine stiffness coefficient. Determine damping coefficient.